Image Reconstruction

Detector response nonuniformity introduces systematic projection errors and ring artifacts in photon-counting detector computed tomography (PCD-CT). In measured PCD-CT data, residual stripe amplitudes vary slowly with projection angle, which fixed-bias models cannot adequately capture. We propose TRACE, a two-stage unsupervised sinogram decomposition method for estimating and correcting these response-related errors. TRACE represents stripes as a fixed bias plus low-order discrete cosine transform (DCT) components, using a small number of coefficients to describe angular variations at each detector element. A learnable analysis--synthesis architecture represents the ideal projections, while two-stage optimization separates them from fixed and then dynamic stripes. An angular-gradient soft orthogonality constraint suppresses correlated variations within the shared DCT gradient subspace, reducing the leakage of object structures into the artifact estimate. All parameters are optimized directly on the measured sinogram without paired training data. Experiments on measured QRM mouse phantom and porcine trotter data show that TRACE suppresses ring artifacts and improves image uniformity while preserving edge sharpness, soft-tissue texture, and trabecular detail.

Ground-penetrating radar (GPR) B-scan image synthesis is important for data augmentation, algorithm validation, and simulation acceleration, yet generating radargrams with both visual realism and physical consistency remains challenging. Existing learning-based generative models often emphasize visual appearance but provide limited control over response geometry. In this paper, we propose PCFlow, a physics-conditioned flow matching framework for fast GPR B-scan image synthesis. The core of PCFlow is a Maxwell-informed dense physical condition field constructed from the parameterized physical model used for electromagnetic simulation, including material properties, target geometry, propagation cues, and response-domain priors. This condition field provides an interpretable interface between physical scene parameters and radar response geometry, and guides conditional flow matching in the VAE latent space toward physically feasible generation paths. We evaluate PCFlow on a gprMax-based buried-pipeline dataset with both in-distribution and out-of-distribution test cases. Experimental results show that PCFlow generates images with more accurate response geometry and high visual fidelity, demonstrating its effectiveness for controllable and physically faithful radar image synthesis.

Intensity-image reconstruction from event streams remains a challenging problem due to the binary, sparse, and asynchronous nature of event data. This work proposes eBIRD, an event-guided reconstruction framework that combines a DDPM with ControlNet-based conditioning. We analyze generic and specialized diffusion learning strategies for handwritten digit (N-MNIST) and face (RGBE-Gaze) reconstruction using 33ms event windows. On N-MNIST, the general model achieves the best reconstruction quality (MSE 0.0052, SSIM 0.8982, PSNR 23.34dB), whereas the specialized model performs best on RGBE-Gaze (MSE 0.0161, SSIM 0.7605, PSNR 19.08dB). These preliminary results suggest that controllable diffusion models are a promising approach for event-guided intensity-image reconstruction, while highlighting that the preferred learning strategy depends on the reconstruction domain.

Inter-crystal scatter (ICS) events pose a significant challenge in ultrahigh- resolution positron emission tomography (UHR-PET), especially as detector crystals become smaller and their readouts increasingly segmented. Current approaches either reject these events, reducing sensitivity, or accept them with suboptimal positioning algorithms, degrading image resolution. We present a feed forward neural network to optimize ICS event recovery by inferring the line-of-response belonging to the first Compton interaction. Our approach was validated using both Monte Carlo simulations and experimental data from the fully pixelated LabPET-IIbased preclinical and brain UHR-PET scanners.Results demonstrate a 70% to 106% increase in sensitivity while preserving sub-millimeter spatial resolvability (down to 1.6 mm) compared to conventional methods. This ICS recovery approach is an effective solution that compensates for the lower detection efficiency of small, pixelated detectors in UHR-PET, enabling reduced scan times and lower radiation doses while largely preserving image quality.

Thermal imaging remains effective under adverse illumination, yet passive long-wave infrared (LWIR) measurements often lack fine texture. Existing thermal texture imaging approaches commonly rely on spectral sensing or registered auxiliary modalities, incurring substantial data throughput or vulnerability to cross-modal degradation. We introduce T$^2$exture, a sparsely perturbed thermal texture imaging framework that aims to reconstruct temporally dense thermal texture sequences from densely sampled passive frames and a few actively perturbed keyframes. We define thermal texture as the residual between a source-on observation and its corresponding source-off passive state. Under sparse LWIR illumination and rapid quasi-steady paired acquisition, this residual attenuates the passive-emission background and approximates a source-induced reflected response, exposing localized material- and geometry-dependent texture. T$^2$exture reconstructs a dense sequence of this source-conditioned response through two stages. Stage 1 estimates the unobserved source-off passive state at each active instant from neighboring passive frames to obtain reliable differential texture anchors. Stage 2 combines sparse anchors with passive structural context near each target time to reconstruct the dense sequence. On the simulated benchmark, T$^2$exture adds only 0.20M parameters to AMT-L while improving PSNR by 6.66 dB. Extensive evaluations on simulated and real acquisitions further show clearer texture recovery and stronger structural preservation than representative VFI baselines. These results establish T$^2$exture as a practical framework for thermal texture imaging under sparse active acquisition.

Many high-resolution imaging systems face the same fundamental question: when have enough measurements been collected to reconstruct an image accurately? We develop Conformalized Rate-Adaptive Sensing (CoRAS), a method that adaptively chooses an acquisition or compression rate for each image while keeping the reconstruction error below a target level with high probability. As measurements are collected, an image reconstruction model gradually recovers the true image, producing a reconstruction path over acquisition rates. CoRAS uses this path up to an early decision time to estimate the target stopping time, defined as the first time at which the reconstruction error falls below the target level. It then calibrates this estimate using images with similar early reconstruction behavior, producing an upper bound on the stopping time with marginal and approximate conditional coverage guarantees. Experiments on image datasets show that CoRAS attains the target stopping-time coverage, uses fewer measurements on average than fixed-rate stopping rules, and assigns more measurements to images that are harder to reconstruct.

Photoacoustic tomography (PAT) combines the optical absorption contrast of biological tissue with the spatial resolution of ultrasound, yet recovering the initial pressure distribution from sparse-view sensor measurements remains an ill-posed inverse problem. Iterative compressive-sensing solvers and unrolled deep networks both retain a dependence on the system matrix at inference, which leaves real-time clinical reconstruction computationally expensive. This paper proposes the Sensor Attention Network (SAN), a Transformer-based architecture that treats the full time series of each sensor as a token and maps raw measurements directly to the reconstructed image without invoking the system matrix at inference. For training and benchmarking, an analytical k-space H-matrix is constructed and validated against the k-Wave pseudo-spectral solver under matched geometry, achieving a mean per-sensor Pearson correlation of 0.919 +/- 0.049, with k-space apodization and Gaussian temporal damping acting synergistically to reduce the energy-normalized mismatch by 49%. Trained with a vessel-weighted loss on 488 augmented samples and evaluated on 46 held-out samples against ISTA, split-Bregman total variation (SBTV), and learned ISTA (LISTA), SAN attains the highest mean SSIM (0.522) and PSNR (22.09 dB) and the lowest NMSE (0.233). Paired t-tests and Wilcoxon signed-rank tests confirm the superiority of SAN over LISTA on PSNR, NMSE, and Pearson correlation at p < 1e-8, and over ISTA and SBTV on all fidelity metrics. By bypassing the H-matrix at inference, SAN reduces reconstruction time by at least an order of magnitude, supporting real-time PAT reconstruction.

Here we introduce ELECTRIC (Evidential Learning-Enhanced CT Reconstruction via Iterative Correction), a physics-guided Bayesian formulation. An evidential neural network provides an image proposal and an error-predictive epistemic-uncertainty surrogate. The latter is converted into an adaptive precision field and inserted into a Poisson-weighted MAP update. The resulting image-evidence-precision-reconstruction loop treats prior confidence as a learned state variable of iterative reconstruction. In addition to the formulation and theoretical analysis, we report two simulation studies on image slices from the AAPM Mayo Clinic Low-Dose CT dataset: a mechanism-validation pilot using transparent surrogate estimators, and a feasibility study in which a trained Normal-Inverse-Gamma evidential network drives the full closed loop. On held-out patients, the learned prior mean reduces reconstruction error by roughly 70 percent relative to filtered back-projection, the learned epistemic uncertainty is error-predictive and supports selective trust, and the physics-guided update restores measurement consistency while the adaptive-precision reconstruction matches or exceeds a validation-tuned fixed prior and remains markedly more robust to prior-strength misspecification. Together these results demonstrate the complete ELECTRIC closed-loop pipeline, while identifying formal uncertainty calibration and joint training as the principal directions for future work.

Trainable denoisers with Lipschitz control have become central to convergent image reconstruction. However, training neural networks that simultaneously offer strong denoising performance and global Lipschitz guarantees is challenging. Existing approaches enforce Lipschitz control only empirically, providing no guarantees beyond the training data. In this work, we show that by exploiting the action of permutations on the image lattice, we can constrain a neural architecture that is globally nonexpansive (Lipschitz bound $\leqslant 1$). We integrate the proposed denoiser with forward imaging operators to develop a reconstruction mechanism that is provably contractive and therefore globally convergent. Experiments on standard inverse problems, such as superresolution and deblurring, demonstrate that our reconstruction performance is competitive with softly constrained baselines while providing Lipschitz guarantees.

Pretrained deep denoisers can be used to solve a wide range of model-based image reconstruction tasks via Plug-and-Play (PnP) and Regularization-by-Denoising (RED) algorithms, without retraining per task. These denoisers are trained only for single-step denoising. Using them as Image Reconstruction (IR) regularizers in an iterative process can destabilize reconstruction. A common failure mode is the peak-and-collapse behaviour: metrics such as PSNR improve for early iterations and then abruptly degrade, making these algorithms unreliable in practice. We propose a data-driven stabilization framework that (i) formalizes this instability of any IR operator through a local quantity and (ii) prevents collapse by regularizing this quantity adaptively, requiring no retraining or modification of the given pretrained network. Our key idea is to control the potentially unstable IR operator with a contractive operator whose stable iterates act as an anchor and prevent collapse. We further introduce an efficient family of trainable contractive operators that serve as strong anchors while remaining lightweight. Extensive experiments across proximal algorithms, denoiser architectures, noise levels, and imaging tasks show consistent, collapse-free performance and improved reliability of PnP and RED reconstruction.

Optical scattering has conventionally been regarded as an impediment in imaging research due to the degradation of image quality during reconstruction. Nevertheless, this study explores two cases in which optical scattering may serve a beneficial role in image reconstruction tasks. We compared the No Scattering MNIST dataset with three Scattering MNIST datasets, each generated under distinct scattering conditions. To assess the information content of the resulting speckle patterns, we employed a Variational Autoencoder (VAE) approach which achieves accuracy comparable to state-of-the-art deep learning approaches, but has an interpretable latent space. We find that scattering can enhance data robustness against spatial pixel loss by effectively distributing information. We also demonstrate that scattering can enable distinctions of focal depth information. We anticipate that these findings will contribute to more efficient imaging techniques, particularly in the presence of obstacles and three-dimensional signals.

Electron microscopy enables nanoscale cellular visualization but faces a trade-off between imaging resolution and acquisition speed. Existing learning-based methods rely on single-stream architectures that struggle to balance perceptual realism and quantitative fidelity, either over-smoothing details or generating unrealistic hallucinations. This work introduces a frequency-adaptive dual-stream architecture to resolve this conflict. Using discrete wavelet transform, we decompose images into low-frequency structures and high-frequency details, then employ a conditional diffusion model for realistic global synthesis and a transformer network for precise detail recovery. Experiments on the EMDiffuse dataset show the method achieves superior LPIPS and resolution ratio, substantially outperforming existing approaches. The method also shows strong generalization across diverse biological samples, supporting fast and reliable electron microscopy imaging for structural biology and nanotechnology applications. The source code and associated dataset are publicly available to facilitate further research.

Cross-modality image translation offers a route to super-resolution fluorescence microscopy from low-resolution images while reducing phototoxicity and instrumentation demands. However, purely data-driven models can produce visually plausible outputs that are inconsistent with optical image formation. Here, we propose a physics-informed generative adversarial network for confocal-to-STED image translation that incorporates microscope-specific point spread function information into the training objective. Simulated and experimentally measured PSFs were evaluated using a limited paired confocal-STED dataset of TOM20-labeled mitochondria in human primary M2 macrophages acquired across different experimental days. Performance was assessed using reference-based and non-reference-based image-quality metrics, together with complementary frequency- and distribution-sensitive analyses. The no-reference metrics probed physics-relevant image properties, including spatial-frequency content, contrast, and signal-to-noise behavior. PSF-guided models improved structural fidelity, reduced local deviations, and achieved closer agreement with STED references than non-PSF baselines, particularly in frequency-domain analyses. These results demonstrate that optical priors can improve the structural fidelity and physical plausibility of generative microscopy models for cross-modality super-resolution imaging.

Event cameras report asynchronous polarity events when changes in log--radiance exceed a fixed contrast threshold, producing signed temporal contrast measurements rather than conventional image frames. We formulate monocular event-based imaging as a synthetic-aperture inverse problem for a static ground-domain log--radiance field $θ\in \mathbb{R}^{N_g}$. Instead of reconstructing a latent pixel-time volume $v \in \mathbb{R}^{N_pN_t}$, we impose the geometric relation $v=Pθ$, where $P$ maps the fixed scene into motion-dependent latent views. Aggregating events over finite time intervals gives the linearized model $$APθ= b+η,$$ where $A$ is a temporal differencing operator, $b$ contains signed binned event counts, and $η$ represents measurement and modeling errors. This decomposition exposes a synthetic-aperture structure: under near-nadir motion, successive projections are approximately shifted views of a common scene, while the composite operator $AP$ remains ill-conditioned because it combines spatial averaging with temporal differencing. We therefore use regularized inversion to recover $θ$. Numerical experiments on simulated data and real near-nadir Falcon Neuro event data show that the proposed $θ$-based formulation recovers coherent large-scale spatial structure, relative to dynamic latent-image and learned event-reconstruction baselines, while suppressing fine-scale texture.

Plug-and-play proximal gradient descent (PnP-PGD) enables flexible image reconstruction by using denoisers as implicit priors. In practice, these denoisers are often deployed outside their training domains. Existing analyses establish convergence under structural assumptions on the deployed denoiser, such as requiring it to be a proximal map or a contraction. However, they do not measure how domain mismatch affects convergence of PnP-PGD. We define this effect as \emph{proximal mismatch}: the discrepancy between a deployed denoiser $\widehat{\mathsf D}$ and a target-domain reference map $\mathsf D_\star=\operatorname{prox}_{R_\star}$ associated with the underlying regularizer $R_\star$. Under this mismatch, each denoising update becomes an inexact proximal step for the target objective. We further derive a stationarity bound that decays at a rate of $\mathcal{O}(1/K)$, with an additive term proportional to the average squared proximal mismatch. This result motivates adaptation via proximal matching rather than MSE-based adaptation alone. We study this approach with two established denoiser families: learned proximal networks and gradient-step denoisers. Experiments on Gaussian deblurring and super-resolution under substantial domain shift show that proximal matching adaptation improves reconstruction quality significantly over MSE-based adaptation, yielding the largest numerical gains in the few-shot regime.

Microscopic urinalysis is a routine diagnostic test at hospitals. Recent studies have demonstrated the effectiveness of deep learning methods to automate microscopic urinalysis. These methods rely on high-quality images of the urine samples in which each cell is clearly identifiable. However, in practice, the urine sample on a glass slide has a multi-layer structure; hence, all the cells are not clearly visible within the depth of field of a lens focused at a particular focal plane. It demands acquiring multiple images at different focal planes to correctly identify each cell in a given urine sample, which is a time-consuming task. In this paper, we propose to simplify the task by recording a video, in place of acquiring multiple images, while gradually changing the focus of the lens manually by hand. A typical length of the video is from 2 to 14 seconds. We reconstruct an all-in-focus image from the recorded video frames and apply a deep learning model to detect and classify urine sediments. As a proof of concept, we conduct experiments on 14 videos acquired by a trained lab technician in a usual diagnostic lab environment and show the effectiveness of the proposed automated urinalysis pipeline with our novel reconstruction algorithm.

Computational imaging, which recovers hidden signals from indirect, noisy measurements, underpins quantitative discovery across scientific disciplines, yet building a correct reconstruction pipeline demands deep domain expertise and remains laborious even for domain scientists. We introduce Imaging-101, a benchmark of 57 expert-verified computational imaging tasks spanning six scientific domains, each grounded in a peer-reviewed paper and canonicalized into a standardized four-stage pipeline (preprocessing, forward physics modeling, inverse solver, and visualization) Three evaluation tracks (planning, function-level unit tests, and end-to-end reconstruction) probe distinct agent capabilities across the full pipeline. Evaluating seven frontier LLMs uncovers systematic challenges in applying coding agents to computational imaging that go beyond those exposed by general coding benchmarks, spanning algorithm selection, physical convention handling, and pipeline integration. These findings highlight concrete capability gaps and point toward skill-augmented, domain-specialized agents as a practical path to reliable computational imaging assistance.

The differentiable shift-variant filtered backprojection (SV-FBP) framework enables data-driven estimation of redundancy weights for cone-beam CT reconstruction under general source trajectories, removing the need for analytically derived weighting schemes. In this work, we present a systematic study of the robustness and adaptability of differentiable SV-FBP under challenging acquisition settings. We show that the framework remains stable across highly irregular and discontinuous trajectories, indicating that reconstruction performance is largely insensitive to trajectory ordering or continuity. Instead, the spatial distribution of sampling points plays a more dominant role. Under sparse-view conditions, differentiable SV-FBP achieves competitive reconstruction quality while providing an order-of-magnitude reduction in computation time compared to iterative reconstruction methods at moderate sampling densities. However, we identify a clear transition regime under severe undersampling, where the absence of iterative data consistency leads to performance degradation. Furthermore, we demonstrate that the framework remains applicable to non-planar multi-isocenter geometries, such as Lissajous-saddle trajectories, without requiring architectural modifications. These findings provide new insights into the behavior and limitations of the differentiable SV-FBP model and highlight it as a flexible and efficient solution for non-standard and robotic CBCT acquisition scenarios.

Subsampling significantly reduces the number of measurements, thereby streamlining data processing and transfer overhead, and shortening acquisition time across diverse real-world applications. The recently introduced Active Deep Probabilistic Subsampling (A-DPS) approach jointly optimizes both the subsampling pattern and the downstream task model, enabling instance- and subject-specific sampling trajectories and effective adaptation to new data at inference time. However, this approach does not fully leverage valuable dataset priors and relies on top-1 sampling, which can impede the optimization process. Herein, we enhance A-DPS by integrating a deterministic (fixed) prior-informed sampling pattern derived from the training dataset, along with group-based sampling via top-k sampling, to achieve more robust optimization, method we call Prior-aware and context-guided Group-based Active DPS (PGA-DPS). We also provide a theoretical analysis supporting improved optimization via group sampling, and validate this with empirical results. We evaluated PGA-DPS on three tasks: classification, image reconstruction, and segmentation, using the MNIST, CIFAR-10, fastMRI knee, and hyperspectral AeroRIT datasets, respectively. In every case, PGA-DPS outperformed A-DPS, DPS, and all other sampling methods.

Lensless imaging enables compact and versatile computational cameras by replacing bulky optics with thin coded elements. However, reconstruction from the resulting measurements is challenging: large-footprint point-spread functions (PSFs) produce highly multiplexed observations, making inversion severely ill-conditioned and sensitive to calibration errors and model mismatch. While deep learning approaches, including hybrid models that incorporate physics priors, have shown promise, explicitly maintaining data fidelity throughout the network hierarchy remains difficult. Here, we propose the Integrated Forward-Inverse Network (IFIN), a physics-guided architecture that interleaves differentiable forward projections with learnable inverse updates at every scale, enabling complementary cues to be exploited jointly in the measurement and image domains. This bidirectional coupling supports progressive, physics-consistent refinement and permits system-constrained PSF kernel adaptation under model uncertainty. On challenging lensless benchmarks, including a newly introduced dataset, IFIN achieves state-of-the-art reconstruction quality. We further observe competitive performance on Gaussian deblurring and simulated inline holography reconstruction, suggesting that the same interleaving principle can extend beyond lensless cameras.

Echo Planar Imaging (EPI) is the standard acquisition technique for diffusion and functional neuroimaging, enabling rapid imaging but suffering from geometric distortions caused by B0 field inhomogeneities. Existing correction methods first reconstruct distorted images using parallel imaging, then estimate the B0 field and correct the distortion in the image domain. In this sequential process, reconstruction artifacts at high acceleration factors and low SNR at high diffusion b-values degrade B0 estimation and limit the overall correction quality. We propose a physics-informed framework that jointly estimates the B0 field and distortion-free image directly from k-space data, without depending on an intermediate parallel-imaging reconstruction for the correction. The image and the B0 field are each represented as a superposition of Gaussian primitives embedded within an MRI physics forward model. The explicit, continuous parameterization captures both smooth regions and tissue boundaries and supports rotated-view EPI acquisitions without interpolation. The diffusion-weighted image is modeled as real and non-negative, with the image phase absorbed into a per-shot phase factor. Rotated views distribute distortions across multiple phase-encoding orientations, improving point spread function isotropy and providing stronger constraints for B0 estimation. On in vivo brain diffusion EPI, the proposed method attains the closest brain-boundary agreement with a distortion-free structural reference, with the largest improvement over sequential methods at high b-value and high acceleration. Extensive visual comparisons further show improved detail fidelity and noise suppression.

X-ray computed tomography reconstruction is an ill-posed inverse problem, particularly in low-dose and sparse-angle settings where measurements are noisy and incomplete. While learned reconstruction methods such as the Learned Primal-Dual algorithm achieve strong performance, they typically rely on supervised training with access to ground-truth data, which is often unavailable in practice. In this work, we propose a self-supervised reconstruction method by extending the Noise2Inverse framework to the Learned Primal-Dual algorithm. The resulting approach, called Noise2Inverse Learned Primal-Dual (N2I-LPD), enables training of a learned iterative reconstruction operator without ground-truth images by exploiting the statistical independence of noise in distinct measurements with respect to angular rotation of the CT-scan. We compare the proposed method with classical reconstruction methods, as well as neural network-based approaches such as a U-Net trained within the same N2I framework. The results demonstrate that N2I-LPD achieves improved reconstruction quality, highlighting the potential of combining learned reconstruction operators with self-supervised training strategies for practical CT imaging scenarios where ground-truth data is unavailable.

In-camera JPEG previews are ubiquitous in raw image formats and provide an sRGB reference at negligible storage cost. Although existing metadata-based reconstruction frameworks can exploit this side information when recovering raw images, their context models often become computationally expensive especially at high resolution, eg, 4K raw image, given that attention mechanisms scale quadratically with feature maps, hindering its practical application. To address these limitations, we propose MambaRaw, a JPEG-conditioned metadata-based raw image reconstruction framework that uses State Space Models (SSMs) to estimate entropy parameters efficiently. Our key contribution comprises a Spatial-Energy Coupled Context Modeling mechanism with two lightweight modules: (1) TileMambaBlock, which performs Mamba-style selective scanning only on information-dense tiles to improve the efficiency; and (2) Energy-Aware Refinement (EAR), an identity-initialized residual module that enhance feature representation to match the long-tail energy distribution of raw signals. Extensive experiments on three camera datasets (Sony, Olympus, Samsung) show consistent improvements over strong metadata-based baselines and set a new state of the art for JPEG-guided raw reconstruction with great efficiency. Notably, at low metadata bitrates, MambaRaw increases PSNR by 1.2--1.4 dB and reduces end-to-end coding latency by about 9%. Code is released at https://github.com/Peizeli1/MambaRaw.

High-quality 3D vehicle assets are essential for autonomous driving simulation. Although multi-view diffusion-based paradigms enable controllable single-image reconstruction, they typically produce limited viewpoints and exhibit cross-view geometric inconsistencies, thereby reducing reconstruction fidelity in real-world scenarios. In this work, we introduce 3DCarGen, a scalable single-view 3D car generation framework designed for real-world images by synthesizing an arbitrary number of 3D-consistent multi-view images. Specifically, given a single image as input, we first synthesize a set of images from fixed viewpoints. These images are then fed into a feed-forward reconstruction model, resulting in a coarse 3D representation based on 3D Gaussian Splatting. Conditioned on this explicit 3D prior, our multi-view diffusion model generates 3D-consistent images from arbitrary camera viewpoints. We further extend a fast mesh reconstruction algorithm by incorporating color-normal joint optimization to recover detailed and coherent 3D vehicle models from the synthesized dense views. Extensive experiments on synthetic and real-world datasets demonstrate that our approach achieves robust geometric consistency and reconstruction fidelity compared to existing methods. Project page: https://honglixiao.github.io/3dcargen.github.io/.

Variational inference (VI) is a powerful method for principled posterior inference for scientific inverse imaging. VI learns the posterior distribution, often with a flow-based network, which can cheaply generate posterior samples upon optimization, and can flexibly incorporate score-based or classic priors. However, its application to large-scale image reconstruction is severely hindered by the poor scalability of the flow-based networks. In this work, we introduce ShuffleFlow, a scalable VI framework to address this challenge. Our method breaks down the problem into three parts: a pixel-unshuffling-based image coordinate sampler, a neural field as feature encoder, and a conditional normalizing flow (CNF) as posterior estimator. Specifically, our framework partitions an image into a stack of sub-images with pixel-unshuffling and uses a shared CNF to model the joint distribution of the sub-image stack. We condition the CNF on the output of a neural field, which embeds feature vectors corresponding to pixel-unshuffling sample locations to capture spatial structures, and share the flow's latent variable across the channels to model their correlations. We demonstrate our method's effectiveness and efficiency on both linear and nonlinear imaging inverse problems, and show its ability to more rapidly generate a high-sample-count posterior than diffusion samplers.

We present GB-LSR (Global-Bandwidth Local Spectral Representation), a fixed-grid local spectral representation for continuous image reconstruction. The image domain is partitioned into non-overlapping square patches, each carrying coefficients for a truncated Fourier basis predicted from shared convolutional-encoder features. A single trainable scalar bandwidth is shared globally across all patches and images, and reconstruction at any continuous coordinate is a fixed-size basis contraction whose cost is independent of image size. We study three bandwidth-handling variants: a trainable global scalar (main), a fixed global scalar, and a per-patch bandwidth field. On a standardized native-reconstruction benchmark across Kodak, Set14, and Urban100, the main variant outperforms matched-budget amortized LIIF / LTE / WIRE re-implementations by 2.8-3.6 dB PSNR and 0.11-0.15 LPIPS, while running at roughly one-quarter of the slowest baseline's inference cost. The single global scalar suffices empirically: per-patch adaptive-bandwidth alternatives do not improve over it on either a closed-form locality diagnostic or an end-to-end ablation. In a separate arbitrary-scale super-resolution (ASR) extension, GB-LSR achieves competitive PSNR-Y under a canonical-style SR protocol and runs 1.44x faster than LIIF-RDN and 3.25x faster than LTE-SwinIR at x4; within the same extension, a variant trained and evaluated without 4-corner local-ensemble averaging gives a 1.77x speedup with 35% lower peak memory and negligible PSNR change, while additionally widening the RDN encoder from 64 to 96 channels gives a small positive PSNR shift with a 1.58x speedup and 31% lower peak memory. Native-reconstruction claims are scoped to the matched-budget amortized protocol, and ASR claims are scoped to a separate canonical-style SR protocol.

We propose a novel Bayesian framework for joint image reconstruction and uncertainty quantification from compressed sensing magnetic resonance imaging data. The problem is formulated as a linear inverse problem, where prior distributions are assigned to the unknown image parameters. Specifically, the image is assumed to be sparse in a given transform domain. We develop a general framework applicable to any sparsifying transform and demonstrate its performance using (1) a total variation transform based on image spatial gradients and (2) a wavelet-domain transform. Bayesian inference is performed using a split-and-augmented Gibbs sampler, while the resulting non-differentiable conditional distributions are efficiently sampled using a proximal Markov chain Monte Carlo method. The proposed algorithms are validated on both single-coil and multi-coil datasets using various k-space sampling patterns and acceleration factors. The results demonstrate that the proposed Bayesian methods consistently outperform their optimisation-based counterparts in image reconstruction while providing uncertainty estimates for the reconstructed images. Furthermore, the estimated uncertainty maps show a strong correlation with the true reconstruction errors and substantially outperformed deep learning-based uncertainty estimation methods.

Tactile imaging seeks to reconstruct the internal structure of soft objects through touch sensing, with applications in medical diagnosis and robotic manipulation. Recent self-supervised learning approaches have shown promising results, but rely on global, unstructured representations and robot-controlled sensing, limiting generalization and practical use. We propose Local Encoder for Spatial Sensing (LESS), an object-centric tactile representation that exploits the local nature of touch. The tactile scene is modeled as a grid of recurrent encoders with local receptive fields, whose states are fused to reconstruct 2D or 3D images of internal structure. This compositional design enables strong generalization: models trained on single-inclusion phantoms accurately image objects with multiple inclusions and varying sizes. The local structure further supports spatial uncertainty estimation. In addition, we enable hand-held tactile imaging via external pose tracking and human-like palpation data, and extend tactile imaging to full 3D reconstruction.

While deep learning has significantly advanced image reconstruction of Electrical Capacitance Tomography (ECT), most data-driven methods map directly between capacitance and permittivity distribution, treating the sensor as a black box. This overlooks the electric potential field -- the fundamental physical link governing the nonlinear and ill-posed ``soft-field'' effect. To address this, we propose an electric potential-augmented ECT benchmark dataset designed to explicitly integrate latent physics behind ECT into the learning process. Generated via a COMSOL-MATLAB pipeline for an eight-electrode sensor as an example, the dataset comprises 20,000 randomized samples across four typical flow patterns. Crucially, alongside the conventional capacitance vectors and permittivity distributions depicted as images, each sample preserves eight excitation-wise full-field potential maps. Beyond data release, we provide illustrative evaluation protocols for both forward and inverse problems of ECT. Through comprehensive testing on both in-distribution (IID) and out-of-distribution (OOD) scenarios, we systematically demonstrate how the inclusion of electric potential maps enhances modeling accuracy and robustness. Fundamentally, the explicit inclusion of latent field information significantly lowers the barrier to integrating physical laws into ECT modeling, thereby establishing a standardized foundation for future physics-guided machine learning of ECT image reconstruction.

Phase retrieval - recovering a complex-valued field from intensity measurements - is typically solved using variants of the Gerchberg-Saxton (GS) algorithm, understood as alternating projections between measurement planes. Meanwhile, modern computational imaging increasingly relies on gradient-based optimization and automatic differentiation. Here we show that these two approaches are mathematically identical: the GS magnitude replacement step is exactly a unit gradient descent step on an amplitude least-squares loss. This equivalence enables seamless integration of classical phase retrieval with differentiable physics pipelines. We further identify two complementary probabilistic interpretations of this equivalence: globally, the amplitude loss is the negative log-likelihood under Gaussian amplitude noise; locally, each projection step arises as a Bayesian update with the propagated field as prior. The local view provides qualitative guidance for relaxation in iterative phase retrieval.

Image Scanning Microscopy (ISM) is a fluorescence imaging technique that combines detector-array acquisition and computational reconstruction to achieve the theoretical resolution of an ideal confocal microscope, i.e., one operating with an infinitesimally small pinhole, while maintaining high signal-to-noise ratio. Among the reconstruction methods for obtaining the super-resolved image, multi-image deconvolution (MID) and its extension aimed at preserving the optical sectioning capability of confocal microscopy, known as super-resolution sectioning ISM (s$^2$ISM), are among the most widely used approaches. Both methods rely on Richardson--Lucy-type iterative schemes, whose semi-convergent behavior requires early stopping and often leads to noise amplification and reconstruction artifacts. In this work, we introduce a self-tuning explicit regularization framework for both MID and s$^2$ISM reconstruction. Within a Bayesian maximum a posteriori formulation, we combine a multi-frame Poisson data fidelity term with explicit regularization, considering $\ell_1$ and smoothed total variation penalties as representative examples. We further develop an automatic and ground-truth-free strategy for regularization parameter selection by adapting the residual whiteness principle to the multi-frame Poisson setting and introducing a spectral high-pass extension tailored to s$^2$ISM. The resulting framework enables stable reconstructions without empirical stopping rules. To demonstrate the proposed framework, we consider first-order optimization schemes based on proximal gradient and mirror descent methods with adaptive backtracking strategies. Experiments on simulated and real fluorescence ISM datasets demonstrate improved reconstruction stability and image quality with respect to unregularized approaches, while enabling robust super-resolution and optical sectioning in low-photon conditions.

Reconstructing physically stable 3D scenes from a single RGB image enables casual images to be converted into simulation-ready digital assets for applications such as immersive interaction and content creation. However, existing single-image reconstruction methods fall short in capturing the physical structure of a scene. As a result, they often produce geometrically plausible but physically inconsistent results, including object floating and penetration, which lead to unstable behavior in physics simulations. Image-conditioned scene generation methods improve physical plausibility but often rely on strong scene priors, yielding plausible yet inaccurate object arrangements that fail to match the input image. We propose REST3D, a single-image reconstruction framework that can reconstruct physically stable 3D scenes by integrating physical scene understanding with physics-constrained refinement. We first introduce an agentic physical scene understanding technique that constructs a scene-tree representation capturing object physical states and inter-object relationships from a gravity-support perspective, providing a structural prior for reconstruction. Leveraging this structure, we initialize the scene using image-to-3D models, followed by scene-tree-guided alignment and physics-constrained optimization to resolve physical violations while preserving visual consistency with the input image. Experiments show that our method significantly reduces physical errors and improves simulation stability on both synthetic and real-world datasets while maintaining strong reconstruction quality. We further demonstrate the reconstructed scenes in VR-based human-object interaction, showing their potential for immersive applications.

Reconstructing visual stimuli from brain recordings has been a meaningful and challenging task in brain decoding. Especially, the achievement of precise and controllable image reconstruction bears great significance in propelling the progress and utilization of brain-computer interfaces. Recent methods, leveraging advances in the power of text-to-image generation models, have reconstructed images that closely approximate complex natural stimuli in terms of semantics (e.g., concepts and objects). However, they struggle to maintain consistency with the original stimuli in fine-grained structural information (e.g., position, orientation and size), which undermines both the controllability and interpretability of the models. To address the aforementioned issues, we propose a two-stage image reconstruction framework, termed MindDiffuser. In Stage 1, Contrastive Language-Image Pretraining (CLIP) text embeddings decoded from brain responses are input into Stable Diffusion, generating a preliminary image containing semantic information. In Stage 2, we use decoded shallow CLIP visual features as supervisory signals, iteratively refining the feature vectors from Stage 1 via backpropagation to align structural information. We conducted extensive experiments on brain response datasets across three modalities (fMRI, EEG, MEG) elicited by visual stimuli, demonstrating that our framework significantly enhances the performance of previous state-of-the-art models, highlighting the effectiveness and versatility of our approach. Spatial and temporal visualization results further support the neurobiological plausibility of our framework, providing guidance for future neural decoding efforts across different brain signal modalities.

Task-based assessment of image quality (IQ) is critically important for the design and optimization of medical imaging systems. Ideal observers, including the Bayesian Ideal Observer (IO) and the ideal linear observer, i.e., the Hotelling observer (HO), provide objective figures of merit (FOMs) that quantify system performance on signal detection tasks. However, the application of ideal observers to high-dimensional image data is often computationally intractable. Channel mechanisms provide an effective framework for dimensionality reduction that can facilitate the computation of ideal observers. This work presents a conjugate gradient (CG)-based method to construct efficient channels for approximating the IO and HO performance.

Starting from the axiomatic formulation of scale-space theory, we develop a viscosity-solution framework for multiscale image representations arising from degenerate elliptic-parabolic partial differential equations. Rather than introducing a new semigroup theory, we work within the standard viscosity-solution setting, using comparison principles to obtain well-posedness, uniqueness, and contraction in the supremum norm. This perspective is used to motivate a hybrid reconstruction operator in which a learned inverse map is followed by a nonlinear diffusion evolution. At the continuous level, the diffusion operator satisfies non-expansiveness, which provides stability for the reconstruction process; this framework is then evaluated on a CT-based mesothelioma classification task, where it attains an AUC of 0.875 with negligible variation across epochs, while the baseline model acquires AUC values from 0.49 to 0.80 without a clear convergence pattern. These observations are consistent with the stabilizing role suggested by the discussed viscosity theory.

Numerous modern applications in signal processing and medical imaging necessitate acquiring high-dimensional signals under tight resource constraints. Traditional sampling theory suggests that accurate signal reconstruction requires a number of measurements proportional to the signal's ambient dimension, a requirement often too expensive or impractical. Compressed sensing challenges this notion by demonstrating that sparse signals can be recovered with fewer measurements, provided the measurement operator meets certain conditions. This proof-of-concept study presents a task-aware flow-based generative framework -- a reformulation of the conventional Flow Matching training paradigm with a flow model trained to optimize subsampling in compressed sensing applications. We establish the fundamental feasibility of the proposed framework of learning subsampling masks that substantially enhance the performance of compressed sensing for image classification, image reconstruction, and MRI acceleration. For the image reconstruction task, our method demonstrated state-of-the-art performance, achieving Peak Signal-to-Noise Ratio of 25.17 dB at the subsampling rate of 5% on the CelebA dataset and 29.24 dB when reconstructing $8\times$ accelerated MRI measurements (fastMRI dataset) with the minimal computational overhead. These results highlight the effectiveness of task-conditioning within generative flow models and reveal a promising direction for representation learning strategies. Overall, the proposed framework offers a unified, flexible approach to designing data- and task-driven sensing schemes that can be potentially adapted to a broad range of inverse problems.

Computational imaging enables compact infrared systems, but deep-learning pipelines that combine image reconstruction and object detection often introduce substantial inference latency. Most existing acceleration strategies compress the reconstruction network while overlooking physical priors from the optical path, leaving a trade-off between accuracy and speed. We present Physics-aware Dual-Integrated Network (PDI-Net), a low-latency framework that integrates infrared reconstruction with object detection and further embeds optical priors into the learning process. PDI-Net uses a supervised U-Net during training, while a semi-U-Net encoder shares features directly with a YOLO-based detector during inference, avoiding full image reconstruction. To bridge the gap between fidelity-oriented reconstruction features and detection-oriented semantics, we introduce a physics-aware large-small bridge (PALS-Bridge), which uses field-dependent point spread function priors to adaptively modulate multiscale convolutional branches. A physics-informed optical degradation simulation pipeline is also developed for training and validation. The method is deployed on a single-lens infrared camera, reducing system weight by about 50% compared with traditional multi-lens designs. On the M3FD benchmark under low-SNR conditions, PDI-Net reduces inference time by 84.06% compared with the Rec+Det with pruning strategy while improving mAP@0.5:0.95 by 5.07%. These results demonstrate compact, low-latency computational infrared imaging for real-time object detection on resource-constrained platforms.

2D Gaussian splatting provides an efficient explicit representation for image reconstruction, but existing methods still require costly per-image iterative optimization or rely on handcrafted priors for primitive allocation. We present AIR, a self-supervised feed-forward framework that amortizes iterative Gaussian fitting into a single network pass, eliminating per-image test-time optimization. AIR adopts a stage-wise residual architecture that progressively predicts additional Gaussian primitives from reconstruction residuals, together with an explicit Stage Control mechanism that activates new primitives only in under-reconstructed regions. A Predict--Optimize--Distill training strategy stabilizes multi-stage prediction by distilling short-horizon optimized Gaussian increments back into the predictor. The stabilized predictor is then jointly finetuned across stages and equipped with an image-adaptive quantizer for compact Gaussian storage. Experiments on Kodak and DIV2K show that AIR achieves better reconstruction quality than representative Gaussian-based baselines while reducing encoding time to 160--300,ms. Code: https://github.com/whoiszzj/AIR.git

To be useful for downstream applications, vision decoding models that are trained to reconstruct seen images from human brain activity must be able to generalize to internally generated visual representations, i.e., mental images. In an analysis of the recently released NSD-Imagery dataset, we demonstrated that while some modern vision decoders can perform quite well on mental image reconstruction, some fail, and that state-of-the-art (SOTA) performance on seen image reconstruction is no guarantee of SOTA performance on mental image reconstruction. Motivated by these findings, we developed MIRAGE, a method explicitly designed to train on vision datasets and cross-decode mental images from brain activity. MIRAGE employs a linear backbone and multi-modal text and image features as input to a diffusion model. Feature metrics and human raters establish MIRAGE as SOTA for mental image reconstruction on the NSD-Imagery benchmark. With ablation analysis we show that mental image reconstruction works best when decoders use image features with relatively few dimensions and include guidance from text-based and both high- and low-level image-based features. Our work indicates that--given the right architecture--existing large-scale datasets using external stimuli are viable training data for decoding mental images, and warrant optimism about the future success and utility of mental image reconstruction.

Extended depth of field microscopy encodes axial information into a single acquisition through engineered point spread functions, but conventional and deep optics approaches are subject to degradation in scattering tissue. We introduce DeepFilters, a scattering-aware deep optics framework that jointly optimizes a parameterized pupil filter and a digital-filter-based reconstruction network through a calibrated differentiable forward model to achieve broad generalization without retraining. Incorporating empirical scattering kernels, physics-guided regularization, and a hybrid genetic-gradient initialization strategy, DeepFilters extends the PSF from 16 micron to >400 micron in clear media and enables signal recovery beyond 120 micron deep in biological tissues, validated across fixed brain slices and sea urchin embryos.

Modern low-field magnetic resonance imaging (MRI) technology offers a compelling alternative to standard high-field MRI, with portable, low-cost systems. However, its clinical utility is limited by a low Signal-to-Noise Ratio (SNR), which hampers diagnostic image quality. A common approach to increase SNR is through repetitive signal acquisitions, known as NEX, but this results in excessively long scan durations. Although recent work has introduced methods to accelerate MRI scans through k-space sampling optimization, the NEX dimension remains unexploited; typically, a single sampling mask is used across all repetitions. Here we introduce NexOP, a deep-learning framework for joint optimization of the sampling and reconstruction in multi-NEX acquisitions, tailored for low-SNR settings. NexOP enables optimizing the sampling density probabilities across the extended k-space-NEX domain, under a fixed sampling-budget constraint, and introduces a new deep-learning architecture for reconstructing a single high-SNR image from multiple low-SNR measurements. Experiments with raw low-field (0.3T) brain data demonstrate that NexOP consistently outperforms competing methods, both quantitatively and qualitatively, across diverse acceleration factors and tissue contrasts. The results also demonstrate that NexOP yields non-uniform sampling strategies, with progressively decreasing sampling across repetitions, hence exploiting the NEX dimension efficiently. Moreover, we present a theoretical analysis supporting these numerical observations. Overall, this work proposes a sampling-reconstruction optimization framework highly suitable for low-field MRI, which can enable faster, higher-quality imaging with low-cost systems and contribute to advancing affordable and accessible healthcare.

Recent event-based image reconstruction methods predominantly rely on Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) to process complementary event information. However, these architectures face fundamental limitations: CNNs often fail to capture global feature correlations, whereas ViTs incur quadratic computational complexity (e.g., $O(n^2)$), hindering their application in high-resolution scenarios. To address these bottlenecks, we introduce EmambaIR, an Efficient visual State Space Model designed for image reconstruction using spatially sparse and temporally continuous event streams. Our framework introduces two key components: the cross-modal Top-k Sparse Attention Module (TSAM) and the Gated State-Space Module (GSSM). TSAM efficiently performs pixel-level top-k sparse attention to guide cross-modal interactions, yielding rich yet sparse fusion features. Subsequently, GSSM utilizes a nonlinear gated unit to enhance the temporal representation of vanilla linear-complexity ($O(n)$) SSMs, effectively capturing global contextual dependencies without the typical computational overhead. Extensive experiments on six datasets across three diverse image reconstruction tasks - motion deblurring, deraining, and High Dynamic Range (HDR) enhancement - demonstrate that EmambaIR significantly outperforms state-of-the-art methods while offering substantial reductions in memory consumption and computational cost. The source code and data are publicly available at: https://github.com/YunhangWickert/EmambaIR

Positron Emission Tomography (PET) image reconstruction is inherently challenged by Poisson noise and physical degradation factors, which are further exacerbated in limited-angle acquisitions. While deep learning methods demonstrate promising performance, their generalization to unseen clinical data distributions remains limited without extensive retraining. We propose PET-Adapter, a test-time domain adaptation framework for generative PET reconstruction models pretrained solely on phantom data. Our method enables adaptation to clinical datasets with varying anatomies, tracers, and scanner configurations without requiring paired ground truth. PET-Adapter introduces layer-wise low-rank anatomical conditioning during adaptation and Ordered Subset Expectation Maximization-based warm-starting that initializes the generation from physics-informed reconstructions, reducing diffusion steps from 50 to 2 without compromising quality. Experiments across multiple clinical datasets demonstrate superior 3D reconstruction performance in both full-angle and limited-angle settings, highlighting the clinical feasibility and computational efficiency of the proposed approach.

Recovering scene color from images captured in scattering media is a fundamental inverse problem in optical imaging. Yet the problem is intrinsically ill-posed as multiple solutions can explain the same observation, and prediction error cannot be controlled without understanding the space of candidate solutions. Here, we present sufficient conditions under which color recovery in a scattering medium becomes well-posed. Observing that ill-posedness stems from (i) projection of spectral signals onto pixel intensities, and (ii) unknown medium parameters, we demonstrate that sensor improvements alone cannot resolve medium-induced distortions without additional constraints. We identify recovery patterns, cross-pixel relationships that naturally occur in images, and prove, for an ideal hyperspectral camera, that they restrict the solution to a unique candidate. This opens the door to a new class of vision algorithms grounded in first principles, enabling quantitative analysis of images in scattering environments.

The generalization performance (GP) of deep learning-based arbitrary-scale image super-resolution (ASISR) methods is subject to limited training datasets and unlimited testing datasets. It is vitally significant to enhance the GP of the pretrained ASISR models by making full use of the testing samples. The ASISR models usually employ an open-loop architecture from low-resolution (LR) images to super-resolution (SR) images. The degradation model from SR samples to LR samples is known bicubic down-sampling for the classical ASISR, is supposed down-sampling with additive random noise for the blind ASISR, and is learnable for the real-world ASISR. Combining the ASISR and degradation models, it is potentially possible to adopt a closed-loop architecture based on the automatic control theory for strengthening the GP of the ASISR methods. Therefore, this paper proposes a closed-loop architecture, circular ASISR (CASISR), to lift the capability of image reconstruction. A mathematical nonlinear loop equation is established to describe the CASISR, the reasonability of the CASISR is proven by conditional probability theory, and the stability of the CASISR is proven by Taylor series approximation. The first-order and second-order absolute difference images are defined to compare the image reconstruction performance of the ASISR and the CASISR methods. Comprehensive simulation experiments show that the proposed CASISR approach outperforms the eight state-of-the-art ASISR approaches in the quality of image reconstruction. Especially, the proposed CASISR is extraordinarily suitable for fractional SR scale factors and is extremely effective for text and stripe images with drastically changed edges.

Iterative ptychographic reconstruction algorithms are widely used for coherent diffractive imaging but can exhibit slow convergence under realistic experimental conditions. We propose a machine learning-augmented approach that accelerates iterative ptychographic reconstruction by introducing a learned fast-forward operator applied during reconstruction. Following an initial warm-up using standard iterations, the fast-forward operator advances the reconstruction toward a more converged state, after which conventional iterative updates are resumed. This strategy preserves the physical consistency and flexibility of established ptychographic solvers while reducing the number of iterations required for convergence. The model is trained on diverse ptychographic datasets and evaluated on experimental data acquired in a different year, demonstrating robustness and temporal generalization. Compared with conventional iterative solvers, the machine learning-augmented method achieves comparable reconstruction quality while converging faster in terms of Poisson negative log-likelihood, yielding over a two-fold reduction in wall-clock time. The approach has been integrated into an existing reconstruction pipeline and deployed in production at a synchrotron beamline, demonstrating practicality for real-time experimental operation.

Traditional iterative reconstruction methods are accurate but computationally expensive, limiting their use in high-throughput and real-time ptychography. Recent deep learning approaches improve speed, but often predict phase as a Euclidean scalar despite its $2π$ periodicity, which can introduce wrapping artifacts, discontinuities at $\pmπ$, and a mismatch between the loss and the underlying signal geometry. We present a deep learning framework for ptychographic reconstruction that models phase on the unit circle using cosine and sine components. Phase error is optimized with a differentiable geodesic loss, which avoids branch-cut discontinuities and provides bounded gradients. The network further incorporates saturation-aware dual-gain input scaling, parallel encoder branches, and three decoders for amplitude, cosine, and sine prediction, together with a composite loss that promotes circular consistency and structural fidelity. Experiments on synthetic and experimental datasets show consistent improvements in both amplitude and phase reconstruction over existing deep learning methods. Frequency-domain analysis further shows better preservation of mid- and high-frequency phase content. The proposed method also provides substantial speedup over iterative solvers while maintaining physically consistent reconstructions.

The Laplacian operator transforms the image into its Laplacian field, which usually is sparse and satisfies a stable distribution. On the other hand, an image can be uniquely reconstructed from its Laplacian field via solving a Poisson equation with a proper boundary condition. Such uniqueness is mathematically guaranteed. Thanks to these properties, we propose to use the sparse Laplacian field to present the image. We first show that the Laplacian field is sparse and satisfies a stable distribution on hundreds images. Then, we show that the image can be accurately reconstruct from its Laplacian field. For the reconstruction task, we propose a shared-kernel wavelet neural network, which solves the Poisson equation and has three advantages. First, it has less than {\bf 0.0002M} parameters, which is compact enough for most of devices. Second, it has linear computation complexity, leading to a real-time reconstruction. Third, it achieves higher accuracy than previous methods. Several numerical experiments are conducted to show the effectiveness and efficiency of the sparse Laplacian field and the proposed Poisson solver. The proposed method can be applied in a large range of applications such as image compression, low light enhancement, object tracking, etc.

This work presents GS-DOT, a novel image reconstruction framework based on Gaussian Splatting (GS) for diffuse optical tomography (DOT). Inspired by GS for rendering applications, absorption coefficients are represented as a sparse sum of anisotropic Gaussian primitives optimized to fit measured time-resolved point-spread functions through analytic gradients and Adam optimization. This is the first adaptation of GS algorithms in the photon diffusion regime, where the ray transport function is replaced by the diffusion functions to enable accurate modeling of light transport in highly scattering media. Validation on synthetic tissue models demonstrate high accuracy in localization and quantification of reconstructed absorption maps for both clean and noisy signals. GS-DOT has demonstrated high robustness to noise and showed a huge reduction in memory demand.

We address the ambiguities in the super-resolution problem under translation. We demonstrate that combinations of low-resolution images at different scales can be used to make the super-resolution problem well posed. Such differences in scale can be achieved using sensors with different pixel sizes (as demonstrated here) or by varying the effective pixel size through changes in optical magnification (e.g., using a zoom lens). We show that images acquired with pairwise coprime pixel sizes lead to a system with a stable inverse, and furthermore, that super-resolution images can be reconstructed efficiently using Fourier domain techniques or iterative least squares methods. Our mathematical analysis provides an expression for the expected error of the least squares reconstruction for large signals assuming i.i.d. noise that elucidates the noise-resolution tradeoff. These results are validated through both one- and two-dimensional experiments that leverage charge-coupled device (CCD) hardware binning to explore reconstructions over a large range of effective pixel sizes. Finally, two-dimensional reconstructions for a series of targets are used to demonstrate the advantages of multiscale super-resolution, and implications of these results for common imaging systems are discussed.

While diffusion priors generate high-quality posterior samples across many inverse problems, they are often trained on limited training sets or purely simulated data, thus inheriting the errors and biases of these underlying sources. Current approaches to finetuning diffusion models rely on a large number of observations with varying forward operators, which can be difficult to collect for many applications, and thus lead to overfitting when the measurement set is small. We propose a method for tuning a prior from only a single observation by combining existing diffusion priors into a single product-of-experts prior and identifying the exponents that maximize the Bayesian evidence. We validate our method on real-world inverse problems, including black hole imaging, where the true prior is unknown a priori, and image deblurring with text-conditioned priors. We find that the evidence is often maximized by priors that extend beyond those trained on a single dataset. By generalizing the prior through exponent weighting, our approach enables posterior sampling from both tempered and combined diffusion models, yielding more flexible priors that improve the trustworthiness of the resulting posterior image distribution.

Retinal laser speckle contrast imaging (LSCI) is a noninvasive optical modality for monitoring retinal blood flow dynamics. However, conventional temporal LSCI (tLSCI) reconstruction relies on sufficiently long speckle sequences to obtain stable temporal statistics, which makes it vulnerable to acquisition disturbances and limits effective temporal resolution. A physically informed reconstruction framework, termed RetinaDiff (Retinal Diffusion Model), is proposed for retinal tLSCI that is robust to motion and requires only a few frames. In RetinaDiff, registration based on phase correlation is first applied to stabilize the raw speckle sequence before contrast computation, reducing interframe misalignment so that fluctuations at each pixel primarily reflect true flow dynamics. This step provides a physics prior corrected for motion and a high quality multiframe tLSCI reference. Next, guided by the physics prior, a conditional diffusion model performs inverse reconstruction by jointly conditioning on the registered speckle sequence and the corrected prior. Experiments on data acquired with a retinal LSCI system developed in house show improved structural continuity and statistical stability compared with direct reconstruction from few frames and representative baselines. The framework also remains effective in a small number of extremely challenging cases, where both the direct 5-frame input and the conventional multiframe reconstruction are severely degraded. Overall, this work provides a practical and physically grounded route for reliable retinal tLSCI reconstruction from extremely limited frames. The source code and model weights will be publicly available at https://github.com/QianChen113/RetinaDiff.

Multi-look acquisition is a widely used strategy for reducing speckle noise in coherent imaging systems such as digital holography. By acquiring multiple measurements, speckle can be suppressed through averaging or joint reconstruction, typically under the assumption that speckle realizations across looks are statistically independent. In practice, however, hardware constraints limit measurement diversity, leading to inter-look correlation that degrades the performance of conventional methods. In this work, we study the reconstruction of speckle-free reflectivity from complex-valued multi-look measurements in the presence of correlated speckle. We model the inter-look dependence using a first-order Markov process and derive the corresponding likelihood under a first-order Markov approximation, resulting in a constrained maximum likelihood estimation problem. To solve this problem, we develop an efficient projected gradient descent framework that combines gradient-based updates with implicit regularization via deep image priors, and leverages Monte Carlo approximation and matrix-free operators for scalable computation. Simulation results demonstrate that the proposed approach remains robust under strong inter-look correlation, achieving performance close to the ideal independent-look scenario and consistently outperforming methods that ignore such dependencies. These results highlight the importance of explicitly modeling inter-look correlation and provide a practical framework for multi-look holographic reconstruction under realistic acquisition conditions. Our code is available at: https://github.com/Computational-Imaging-RU/MLE-Holography-Markov.

We study the deep image prior (DIP) framework applied to photoacoustic tomography (PAT) as an unsupervised reconstruction approach to mitigate limited-view artifacts and noise commonly encountered in experimental settings. Efficient implementation is achieved by employing recently published fast forward and adjoint algorithms for circular measurement geometries. Initialization via a fast inverse and total variation (TV) regularization are applied to further suppress noise and mitigate overfitting. For comparison, we compute a classical TV reconstruction. Our experiments comprise simulated PAT measurements under limited-view geometries and varying levels of added noise as well as experimental measurements together with using a digital twin for quality assessment. Our findings suggest that DIP framework provides an effective unsupervised strategy for robust PAT reconstruction even in the challenging case of a limited view geometry providing improvement in several quantitative measures over total variation reconstructions.

Radio astronomy plays a crucial role in understanding the universe, particularly within the realm of non-thermal astrophysics. Images of celestial objects are derived from the signals (called visibility) measured by radio telescopes. Such imaging results, called dirty images, contain artifacts due to factors such as sparsity and therefore require reconstruction to improve imaging quality. Existing methods typically restrict reconstruction to a unimodal domain, either to the dirty image after imaging or to the sparse visibility prior to imaging. Focusing solely on each unimodal reconstruction results in the loss of complementary in-context information in either the visibility or image domain, leading to an incomplete modeling of mutual dependency and consistency. To address these challenges, we propose CDCRec, a multimodal radio interferometric data reconstruction method that explicitly models cross-domain consistency. We design a hierarchical multi-task and multi-stage framework to enhance the exploration of interplays between domains during reconstruction. Our experimental results demonstrate that CDCRec improves imaging performance through enhanced cross-domain correlation extraction. In particular, our self-supervised complementary modeling strategy is better than current methods at interferometric domain translations that rely heavily on recovering dense information from constrained source-domain data.

Photoacoustic tomography (PAT) is an emerging imaging modality that combines the complementary strengths of optical contrast and ultrasonic resolution. A central task is image reconstruction, where measured acoustic signals are used to recover the initial pressure distribution. For ideal point-like or line-like detectors, several efficient and fast reconstruction algorithms exist, including Fourier methods, filtered backprojection, and time reversal. However, when applied to data acquired with finite-size detectors, these methods yield systematically blurred images. Although sharper images can be obtained by compensating for finite-detector effects, supervised learning approaches typically require ground-truth images that may not be available in practice. We propose a self-supervised reconstruction method based on Noisier2Inverse that addresses finite-size detector effects without requiring ground-truth data. Our approach operates directly on noisy measurements and learns to recover high-quality PAT images in a ground-truth-free manner. Its key components are: (i) PAT-specific modeling that recasts the problem as angular deblurring; (ii) a Noisier2Inverse formulation in the polar domain that leverages the known angular point-spread function; and (iii) a novel, statistically grounded early-stopping rule. In experiments, the proposed method consistently outperforms alternative approaches that do not use supervised data and achieves performance close to supervised benchmarks, while remaining practical for real acquisitions with finite-size detectors.

Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches, which have primarily addressed denoising and, more recently, linear inverse problems. We address nonlinear inverse problems and introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images. SPLIT enforces cross-partition consistency and measurement-domain fidelity while exploiting complementary information across multiple partitions. Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation. We regularize training with an automatic stopping rule that halts optimization when a no-reference image-quality surrogate saturates. As a concrete application, we derive SPLIT variants for multispectral computed tomography. Experiments on sparse-view acquisitions demonstrate high reconstruction quality and robustness to noise, surpassing classical iterative reconstruction and recent self-supervised baselines.

A long-term goal in CT imaging is to achieve fast and accurate 3D reconstruction from sparse-view projections, thereby reducing radiation exposure, lowering system cost, and enabling timely imaging in clinical workflows. Recent feed-forward approaches have shown strong potential toward this overarching goal, yet their results still suffer from artifacts and loss of fine details. In this work, we introduce Iterative Latent Volumes (ILV), a feed-forward framework that integrates data-driven priors with classical iterative reconstruction principles to overcome key limitations of prior feed-forward models in sparse-view CBCT reconstruction. At its core, ILV constructs an explicit 3D latent volume that is repeatedly updated by conditioning on multi-view X-ray features and the learned anatomical prior, enabling the recovery of fine structural details beyond the reach of prior feed-forward models. In addition, we develop and incorporate several key architectural components, including an X-ray feature volume, group cross-attention, efficient self-attention, and view-wise feature aggregation, that efficiently realize its core latent volume refinement concept. Extensive experiments on a large-scale dataset of approximately 14,000 CT volumes demonstrate that ILV significantly outperforms existing feed-forward and optimization-based methods in both reconstruction quality and speed. These results show that ILV enables fast and accurate sparse-view CBCT reconstruction suitable for clinical use. The project page is available at: https://sngryonglee.github.io/ILV/.

To develop a deep-learning method for achieving fast high-resolution MR elastography from highly undersampled data without the need of high-quality training dataset. We first framed the deep neural network representation as a nonlinear extension of the linear subspace model, then used it to represent and reconstruct MRE image repetitions from undersampled k-space data. The network weights were learned using a multi-level k-space consistent loss. To further enhance reconstruction quality, phase-contrast specific magnitude and phase priors were incorporated, including the similarity of anatomical structures and smoothness of wave-induced harmonic displacement. Experiments were conducted using both 3D gradient-echo spiral and multi-slice spin-echo spiral MRE datasets. Compared to the conventional linear subspace-based approaches, the nonlinear network representation method was able to produce superior image reconstruction with suppressed noise and artifacts from a single in-plane spiral arm per MRE repetition (e.g., 2mm isotropic resolution in 1 min with a total R=10), yielding comparable stiffness estimation to the fully sampled data. This work demonstrated the feasibility of using deep network representations to model and reconstruct MRE images from highly-undersampled data, a nonlinear extension of the subspace-based approaches.

Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation algorithms for solving variational problems. While the underlying algorithm is usually formulated in the functional analytic setting, learned approaches are often viewed as purely discrete. In this survey we present a unified operator view for learned iterative networks. Specifically, we formulate a learned reconstruction operator, defining how to compute, and separately the learning problem, which defines what to compute. In this setting we present common approaches and show that many approaches are closely related in their core. We review linear as well as non-linear inverse problems in this framework and present a short numerical study to conclude.