Computational Imaging

Designing a computational imaging system -- selecting operators, setting parameters, validating consistency -- requires weeks of specialist effort per modality, creating an expertise bottleneck that excludes the broader scientific community from prototyping imaging instruments. We introduce spec.md, a structured specification format, and three autonomous agents -- Plan, Judge, and Execute -- that translate a one-sentence natural-language description into a validated forward model with bounded reconstruction error. A design-to-real error theorem decomposes total reconstruction error into five independently bounded terms, each linked to a corrective action. On 6 real-data modalities spanning all 5 carrier families, the automated pipeline matches expert-library quality (98.1 +/- 4.2%). Ten novel designs -- composing primitives into chains from 3D to 5D -- demonstrate compositional reach beyond any single-modality tool.

Real-time monitoring of high-energy propellant combustion is difficult. Extreme high dynamic range (HDR), microsecond-scale particle motion, and heavy smoke often occur together. These conditions drive saturation, motion blur, and unstable particle extraction in conventional imaging. We present a closed-loop Event--SVE measurement system that couples a spatially variant exposure (SVE) camera with a stereo pair of neuromorphic event cameras. The SVE branch produces HDR maps with an explicit smoke-aware fusion strategy. A multi-cue smoke-likelihood map is used to separate particle emission from smoke scattering, yielding calibrated intensity maps for downstream analysis. The resulting HDR maps also provide the absolute-intensity reference missing in event cameras. This reference is used to suppress smoke-driven event artifacts and to improve particle-state discrimination. Based on the cleaned event observations, a stereo event-based 3D pipeline estimates separation height and equivalent particle size through feature extraction and triangulation (maximum calibration error 0.56%). Experiments on boron-based propellants show multimodal equivalent-radius statistics. The system also captures fast separation transients that are difficult to observe with conventional sensors. Overall, the proposed framework provides a practical, calibration-consistent route to microsecond-resolved 3D combustion measurement under smoke-obscured HDR conditions.

Burst image restoration aims to reconstruct a high-quality image from burst images, which are typically captured using manually designed exposure settings. Although these exposure settings significantly influence the final restoration performance, the problem of finding optimal exposure settings has been overlooked. In this paper, we present Dynamic Exposure Burst Image Restoration (DEBIR), a novel burst image restoration pipeline that enhances restoration quality by dynamically predicting exposure times tailored to the shooting environment. In our pipeline, Burst Auto-Exposure Network (BAENet) estimates the optimal exposure time for each burst image based on a preview image, as well as motion magnitude and gain. Subsequently, a burst image restoration network reconstructs a high-quality image from burst images captured using these optimal exposure times. For training, we introduce a differentiable burst simulator and a three-stage training strategy. Our experiments demonstrate that our pipeline achieves state-of-the-art restoration quality. Furthermore, we validate the effectiveness of our approach on a real-world camera system, demonstrating its practicality.

Despite offering high sensitivity, a high signal-to-noise ratio, and a broad spectral range, single-pixel imaging (SPI) is limited by low measurement efficiency and long data-acquisition times. To address this, we propose a wavelength-multiplexed, spatially incoherent diffractive optical processor combined with a compact/shallow digital artificial neural network (ANN) to implement compressive SPI. Specifically, we model the bucket detection process in conventional SPI as a linear intensity transformation with spatially and spectrally varying point-spread functions. This transformation matrix is treated as a learnable parameter and jointly optimized with a shallow digital ANN composed of 2 hidden nonlinear layers. The wavelength-multiplexed diffractive processor is then configured via data-free optimization to approximate this pre-trained transformation matrix; after this optimization, the diffractive processor remains static/fixed. Upon multi-wavelength illumination and diffractive modulation, the target spatial information of the input object is spectrally encoded. A single-pixel detector captures the output spectral power at each illumination band, which is then rapidly decoded by the jointly trained digital ANN to reconstruct the input image. In addition to our numerical analyses demonstrating the feasibility of this approach, we experimentally validated its proof-of-concept using an array of light-emitting diodes (LEDs). Overall, this work demonstrates a computational imaging framework for compressive SPI that can be useful in applications such as biomedical imaging, autonomous devices, and remote sensing.

We introduce SpiderCam, an FPGA-based snapshot depth-from-defocus camera which produces 480x400 sparse depth maps in real-time at 32.5 FPS over a working range of 52 cm while consuming 624 mW of power in total. SpiderCam comprises a custom camera that simultaneously captures two differently focused images of the same scene, processed with a SystemVerilog implementation of depth from differential defocus (DfDD) on a low-power FPGA. To achieve state-of-the-art power consumption, we present algorithmic improvements to DfDD that overcome challenges caused by low-power sensors, and design a memory-local implementation for streaming depth computation on a device that is too small to store even a single image pair. We report the first sub-Watt total power measurement for passive FPGA-based 3D cameras in the literature.

Polarization imaging is a technique that creates a pixel map of the polarization state in a scene. Although invisible to the human eye, polarization can assist various sensing and computer vision tasks. Existing polarization cameras use spatial or temporal multiplexing, which increases the camera volume, weight, cost, or all of the above. Recent lensless imaging approaches, such as DiffuserCam, have demonstrated that compact imaging systems can be realized by replacing the lens with a coding element and performing computational reconstruction. In this work, we propose a compact lensless polarization camera composed of a diffuser and a simple striped polarization mask. By combining this optical design with a reconstruction algorithm that explicitly models the polarization-encoded lensless measurements, four linear polarization images are recovered from a single snapshot. Our results demonstrate the potential of lensless approaches for polarization imaging and reveal the physical factors that govern reconstruction quality, guiding the development of high-quality practical systems.

Existing computational spectral imaging systems typically rely on coded aperture and beam splitters that block a substantial fraction of incident light, degrading reconstruction quality under light-starved conditions. To address this limitation, we develop the Oscillating Dispersion Imaging Spectrometer (ODIS), which for the first time achieves near-full light throughput by axially translating a disperser between the conjugate image plane and a defocused position, sequentially capturing a panchromatic (PAN) image and a dispersed measurement along a single optical path. We further propose a PAN-guided Dispersion-Aware Deep Unfolding Network (PDAUN) that recovers high-fidelity spectral information from maskless dispersion under PAN structural guidance. Its data-fidelity step derives an FFT-Woodbury preconditioned solver by exploiting the cyclic-convolution property of the ODIS forward model, while a Dispersion-Aware Deformable Convolution module (DADC) corrects sub-pixel spectral misalignment using PAN features. Experiments show state-of-the-art performance on standard benchmarks, and cross-system comparisons confirm that ODIS yields decisive gains under low illumination. High-fidelity reconstruction is validated on a physical prototype.

This work introduces and demonstrates the first system capable of imaging fast-moving extended non-rigid objects through strong atmospheric turbulence at high frame rate. Event cameras are a novel sensing architecture capable of estimating high-speed imagery at thousands of frames per second. However, on their own event cameras are unable to disambiguate scene motion from turbulence. In this work, we overcome this limitation using event-based light field cameras: By simultaneously capturing multiple views of a scene, event-based light field cameras and machine learning-based reconstruction algorithms are able to disambiguate motion-induced dynamics, which produce events that are strongly correlated across views, from turbulence-induced dynamics, which produce events that are weakly correlated across view. Tabletop experiments demonstrate event-based light field can overcome strong turbulence while imaging high-speed objects traveling at up to 16,000 pixels per second.

Computational imaging systems -- from coded-aperture cameras to cryo-electron microscopes -- span five carrier families yet share a hidden structural simplicity. We prove that every imaging forward model decomposes into a directed acyclic graph over exactly 11 physically typed primitives (Finite Primitive Basis Theorem) -- a sufficient and minimal basis that provides a compositional language for designing any imaging modality. We further prove that every reconstruction failure has exactly three independent root causes: information deficiency, carrier noise, and operator mismatch (Triad Decomposition). The three gates map to the system lifecycle: Gates 1 and 2 guide design (sampling geometry, carrier selection); Gate 3 governs deployment-stage calibration and drift correction. Validation across 12 modalities and all five carrier families confirms both results, with +0.8 to +13.9 dB recovery on deployed instruments. Together, the 11 primitives and 3 gates establish the first universal grammar for designing, diagnosing, and correcting computational imaging systems.

Prevalent Computational Aberration Correction (CAC) methods are typically tailored to specific optical systems, leading to poor generalization and labor-intensive re-training for new lenses. Developing CAC paradigms capable of generalizing across diverse photographic lenses offers a promising solution to these challenges. However, efforts to achieve such cross-lens universality within consumer photography are still in their early stages due to the lack of a comprehensive benchmark that encompasses a sufficiently wide range of optical aberrations. Furthermore, it remains unclear which specific factors influence existing CAC methods and how these factors affect their performance. In this paper, we present comprehensive experiments and evaluations involving 24 image restoration and CAC algorithms, utilizing our newly proposed UniCAC, a large-scale benchmark for photographic cameras constructed via automatic optical design. The Optical Degradation Evaluator (ODE) is introduced as a novel framework to objectively assess the difficulty of CAC tasks, offering credible quantification of optical aberrations and enabling reliable evaluation. Drawing on our comparative analysis, we identify three key factors -- prior utilization, network architecture, and training strategy -- that most significantly influence CAC performance, and further investigate their respective effects. We believe that our benchmark, dataset, and observations contribute foundational insights to related areas and lay the groundwork for future investigations. Benchmarks, codes, and Zemax files will be available at https://github.com/XiaolongQian/UniCAC.

Pattern recognition and image classification are essential tasks in machine vision. Autonomous vehicles, for example, require being able to collect the complex information contained in a changing environment and classify it in real time. Here, we experimentally demonstrate image classification at multi-kHz frame rates combining the technique of single pixel imaging (SPI) with a low complexity machine learning model. The use of a microLED-on-CMOS digital light projector for SPI enables ultrafast pattern generation for sub-ms image encoding. We investigate the classification accuracy of our experimental system against the broadly accepted benchmarking task of the MNIST digits classification. We compare the classification performance of two machine learning models: An extreme learning machine (ELM) and a backpropagation trained deep neural network. The complexity of both models is kept low so the overhead added to the inference time is comparable to the image generation time. Crucially, our single pixel image classification approach is based on a spatiotemporal transformation of the information, entirely bypassing the need for image reconstruction. By exploring the performance of our SPI based ELM as binary classifier we demonstrate its potential for efficient anomaly detection in ultrafast imaging scenarios.

Projection mapping (PM) enables augmented reality (AR) experiences without requiring users to wear head-mounted displays and supports multi-user interaction. It is regarded as a promising technology for a variety of applications in which users interact with content superimposed onto augmented objects in tabletop workspaces, including remote collaboration, healthcare, industrial design, urban planning, artwork creation, and office work. However, conventional PM systems often suffer from projection shadows when users occlude the light path. Prior approaches employing multiple distributed projectors can compensate for occlusion, but suffer from latency due to computational processing, degrading the user experience. In this research, we introduce a synthetic-aperture PM system that uses a significantly larger number of projectors, arranged densely in the environment, to achieve delay-free, shadowless projection for tabletop workspaces without requiring computational compensation. To address spatial resolution degradation caused by subpixel misalignment among overlaid projections, we develop and validate an offline blur compensation method whose computation time remains independent of the number of projectors. Furthermore, we demonstrate that our shadowless PM plays a critical role in achieving a fundamental goal of PM: altering material properties without evoking projection-like impression. Specifically, we define this perceptual impression as ``sense of projection (SoP)'' and establish a PM design framework to minimize the SoP based on user studies.

Pore-scale imaging of subsurface formations is costly and limited to discrete depths, creating significant gaps in reservoir characterization. To address this, we present a conditional Generative Adversarial Network (cGAN) framework for synthesizing realistic thin section images of carbonate rock formations, conditioned on porosity values derived from well logs. The model is trained on 5,000 sub-images extracted from 15 petrography samples over a depth interval of 1992-2000m, the model generates geologically consistent images across a wide porosity range (0.004-0.745), achieving 81% accuracy within a 10% margin of target porosity values. The successful integration of well log data with the trained generator enables continuous pore-scale visualization along the wellbore, bridging gaps between discrete core sampling points and providing valuable insights for reservoir characterization and energy transition applications such as carbon capture and underground hydrogen storage.

Time-of-Flight non-line-of-sight (ToF NLOS) imaging techniques provide state-of-the-art reconstructions of scenes hidden around corners by inverting the optical path of indirect photons scattered by visible surfaces and measured by picosecond resolution sensors. The emergence of a wide range of ToF NLOS imaging methods with heterogeneous formulae and hardware implementations obscures the assessment of both their theoretical and experimental aspects. We present a comprehensive study of a representative set of ToF NLOS imaging methods by discussing their similarities and differences under common formulation and hardware. We first outline the problem statement under a common general forward model for ToF NLOS measurements, and the typical assumptions that yield tractable inverse models. We discuss the relationship of the resulting simplified forward and inverse models to a family of Radon transforms, and how migrating these to the frequency domain relates to recent phasor-based virtual line-of-sight imaging models for NLOS imaging that obey the constraints of conventional lens-based imaging systems. We then evaluate performance of the selected methods on hidden scenes captured under the same hardware setup and similar photon counts. Our experiments show that existing methods share similar limitations on spatial resolution, visibility, and sensitivity to noise when operating under equal hardware constraints, with particular differences that stem from method-specific parameters. We expect our methodology to become a reference in future research on ToF NLOS imaging to obtain objective comparisons of existing and new methods.

Ptychography is a computational imaging technique widely used for high-resolution materials characterization, but high-quality reconstructions often require the use of regularization functions that largely remain manually designed. We introduce Ptychi-Evolve, an autonomous framework that uses large language models (LLMs) to discover and evolve novel regularization algorithms. The framework combines LLM-driven code generation with evolutionary mechanisms, including semantically-guided crossover and mutation. Experiments on three challenging datasets (X-ray integrated circuits, low-dose electron microscopy of apoferritin, and multislice imaging with crosstalk artifacts) demonstrate that discovered regularizers outperform conventional reconstructions, achieving up to +0.26 SSIM and +8.3~dB PSNR improvements. Besides, Ptychi-Evolve records algorithm lineage and evolution metadata, enabling interpretable and reproducible analysis of discovered regularizers.

Mobile photography is often limited by complex, lens-specific optical aberrations. While recent deep learning methods approach this as an end-to-end deblurring task, these "black-box" models lack explicit optical modeling and can hallucinate details. Conversely, classical blind deconvolution remains highly unstable. To bridge this gap, we present Lens2Zernike, a deep learning framework that blindly recovers physical optical parameters from a single blurred image. To the best of our knowledge, no prior work has simultaneously integrated supervision across three distinct optical domains. We introduce a novel physics-consistent strategy that explicitly minimizes errors via direct Zernike coefficient regression (z), differentiable physics constraints encompassing both wavefront and point spread function derivations (p), and auxiliary multi-task spatial map predictions (m). Through an ablation study on a ResNet-18 backbone, we demonstrate that our full multi-task framework (z+p+m) yields a 35% improvement over coefficient-only baselines. Crucially, comparative analysis reveals that our approach outperforms two established deep learning methods from previous literature, achieving significantly lower regression errors. Ultimately, we demonstrate that these recovered physical parameters enable stable non-blind deconvolution, providing substantial in-domain improvement on the patented Institute for Digital Molecular Analytics and Science (IDMxS) Mobile Camera Lens Database for restoring diffraction-limited details from severely aberrated mobile captures.

State-of-the-art EfficientSCI loses 20.58 dB when its assumed forward operator deviates from physical reality in just eight parameters, yet no existing benchmark quantifies operator mismatch, the default condition in deployed compressive imaging systems. We introduce InverseNet, the first cross-modality benchmark for operator mismatch, spanning CASSI, CACTI, and single-pixel cameras. Evaluating 12 methods under a four-scenario protocol (ideal, mismatched, oracle-corrected, blind calibration) across 27 simulated scenes and 9 real hardware captures, we find: (1) deep learning methods lose 10-21 dB under mismatch, eliminating their advantage over classical baselines; (2) performance and robustness are inversely correlated across modalities (Spearman r_s = -0.71, p < 0.01); (3) mask-oblivious architectures recover 0% of mismatch losses regardless of calibration quality, while operator-conditioned methods recover 41-90%; (4) blind grid-search calibration recovers 85-100% of the oracle bound without ground truth. Real hardware experiments confirm that simulation trends transfer to physical data. Code will be released upon acceptance.

Multispectral demosaicing is crucial to reconstruct full-resolution spectral images from snapshot mosaiced measurements, enabling real-time imaging from neurosurgery to autonomous driving. Classical methods are blurry, while supervised learning requires costly ground truth (GT) obtained from slow line-scanning systems. We propose Perspective-Equivariant Fine-tuning for Demosaicing (PEFD), a framework that learns multispectral demosaicing from mosaiced measurements alone. PEFD a) exploits the projective geometry of camera-based imaging systems to leverage a richer group structure than previous demosaicing methods to recover more null-space information, and b) learns efficiently without GT by adapting pretrained foundation models designed for 1-3 channel imaging. On surgical and automotive datasets, PEFD recovers fine details such as blood vessels and preserves spectral fidelity, substantially outperforming recent approaches, nearing supervised performance. Furthermore, the performance of PEFD is demonstrated on raw, unprocessed data from a commercial multispectral sensor. Code is at https://github.com/Andrewwango/pefd.

Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction relies on Stochastic Differential Equations (SDEs) for forward diffusion and reverse denoising, where such stochasticity can interfere with repeated data consistency corrections in CT reconstruction. Since CT reconstruction is often time-critical in clinical and interventional scenarios, improving reconstruction efficiency is essential. In contrast, Flow Matching (FM) models sampling as a deterministic Ordinary Differential Equation (ODE), yielding smooth trajectories without stochastic noise injection. This deterministic formulation is naturally compatible with repeated data consistency operations. Furthermore, we observe that FM-predicted velocity fields exhibit strong correlations across adjacent steps. Motivated by this, we propose an FM-based CT reconstruction framework (FMCT) and an efficient variant (EFMCT) that reuses previously predicted velocity fields over consecutive steps to substantially reduce the number of Neural network Function Evaluations (NFEs), thereby improving inference efficiency. We provide theoretical analysis showing that the error introduced by velocity reuse is bounded when combined with data consistency operations. Extensive experiments demonstrate that FMCT/EFMCT achieve competitive reconstruction quality while significantly improving computational efficiency compared with diffusion-based methods. The codebase is open-sourced at https://github.com/EFMCT/EFMCT.

We propose Coded-E2LF (coded event to light field), a computational imaging method for acquiring a 4-D light field using a coded aperture and a stationary event-only camera. In a previous work, an imaging system similar to ours was adopted, but both events and intensity images were captured and used for light field reconstruction. In contrast, our method is purely event-based, which relaxes restrictions for hardware implementation. We also introduce several advancements from the previous work that enable us to theoretically support and practically improve light field reconstruction from events alone. In particular, we clarify the key role of a black pattern in aperture coding patterns. We finally implemented our method on real imaging hardware to demonstrate its effectiveness in capturing real 3-D scenes. To the best of our knowledge, we are the first to demonstrate that a 4-D light field with pixel-level accuracy can be reconstructed from events alone. Our software and supplementary video are available from our project website.

We present Lumosaic, a compact active hyperspectral video system designed for real-time capture of dynamic scenes. Our approach combines a narrowband LED array with a coded-exposure-pixel (CEP) camera capable of high-speed, per-pixel exposure control, enabling joint encoding of scene information across space, time, and wavelength within each video frame. Unlike passive snapshot systems that divide light across multiple spectral channels simultaneously and assume no motion during a frame's exposure, Lumosaic actively synchronizes illumination and pixel-wise exposure, improving photon utilization and preserving spectral fidelity under motion. A learning-based reconstruction pipeline then recovers 31-channel hyperspectral (400-700 nm) video at 30 fps and VGA resolution, producing temporally coherent and spectrally accurate reconstructions. Experiments on synthetic and real data demonstrate that Lumosaic significantly improves reconstruction fidelity and temporal stability over existing snapshot hyperspectral imaging systems, enabling robust hyperspectral video across diverse materials and motion conditions.

Computational imaging forward models, from coded aperture spectral cameras to MRI scanners, are traditionally implemented as monolithic, modality-specific codes. We prove that every forward model in a broad, precisely defined operator class Cimg (encompassing clinical, scientific, and industrial imaging modalities, both linear and nonlinear) admits an epsilon-approximate representation as a typed directed acyclic graph (DAG) whose nodes are drawn from a library of exactly 11 canonical primitives: Propagate, Modulate, Project, Encode, Convolve, Accumulate, Detect, Sample, Disperse, Scatter, and Transform. We call this the Finite Primitive Basis Theorem. The proof is constructive: we provide an algorithm that, given any H in Cimg, produces a DAG G with relative operator error at most epsilon and graph complexity within prescribed bounds. We further prove that the library is minimal: removing any single primitive causes at least one modality to lose its epsilon-approximate representation. A systematic analysis of nonlinearities in imaging physics shows they fall into two structural categories: pointwise scalar functions (handled by Transform) and self-consistent iterations (unrolled into existing linear primitives). Empirical validation on 31 linear modalities confirms eimg below 0.01 with at most 5 nodes and depth 5, and we provide constructive DAG decompositions for 9 additional nonlinear modalities. These results establish mathematical foundations for the Physics World Model (PWM) framework.

Capturing high-quality images from only a few detected photons is a fundamental challenge in computational imaging. Single-photon avalanche diode (SPAD) sensors promise high-quality imaging in regimes where conventional cameras fail, but raw quanta frames contain only sparse, noisy, binary photon detections. Recovering a coherent image from a burst of such frames requires handling alignment, denoising, and demosaicing (for color) under noise statistics far outside those assumed by standard restoration pipelines or modern generative models. We present an approach that adapts large text-to-image latent diffusion models to the photon-limited domain of quanta burst imaging. Our method leverages the structural and semantic priors of internet-scale diffusion models while introducing mechanisms to handle Bernoulli photon statistics. By integrating latent-space restoration with burst-level spatio-temporal reasoning, our approach produces reconstructions that are both photometrically faithful and perceptually pleasing, even under high-speed motion. We evaluate the method on synthetic benchmarks and new real-world datasets, including the first color SPAD burst dataset and a challenging Deforming (XD) video benchmark. Across all settings, the approach substantially improves perceptual quality over classical and modern learning-based baselines, demonstrating the promise of adapting large generative priors to extreme photon-limited sensing. Code at https://github.com/Aryan-Garg/gQIR.

We investigate the application of the common circle method for estimating sample motion in optical diffraction tomography (ODT) of sub-millimeter sized biological tissue. When samples are confined via contact-free acoustical force fields, their motion must be estimated from the captured images. The common circle method identifies intersections of Ewald spheres in Fourier space to determine rotational motion. This paper presents a practical implementation, incorporating temporal consistency constraints to achieve stable reconstructions. Our results on both simulated and real-world data demonstrate that the common circle method provides a computationally efficient alternative to full optimization methods for motion detection.

Gamma-ray bursts (GRBs) are among the most energetic transient phenomena in the universe and serve as powerful probes for high-energy astrophysical processes. In particular, faint GRBs originating from a distant universe may provide unique insights into the early stages of star formation. However, detecting and localizing such weak sources remains challenging owing to low photon statistics and substantial background noise. Although recent machine learning models address individual aspects of these challenges, they often struggle to balance the trade-off between statistical robustness and noise suppression. Consequently, we propose ComptonUNet, a hybrid deep learning framework that jointly processes raw data and reconstructs images for robust GRB localization. ComptonUNet was designed to operate effectively under conditions of limited photon statistics and strong background contamination by combining the statistical efficiency of direct reconstruction models with the denoising capabilities of image-based architectures. We perform realistic simulations of GRB-like events embedded in background environments representative of low-Earth orbit missions to evaluate the performance of ComptonUNet. Our results demonstrate that ComptonUNet significantly outperforms existing approaches, achieving improved localization accuracy across a wide range of low-statistic and high-background scenarios.

Though there exists a reasonable forward model for blur based on optical physics, recovering depth from a collection of defocused images remains a computationally challenging optimization problem. In this paper, we show that with contemporary optimization methods and reasonable computing resources, a global optimization approach to depth from defocus is feasible. Our approach rests on alternating minimization. When holding the depth map fixed, the forward model is linear with respect to the all-in-focus image. When holding the all-in-focus image fixed, the depth at each pixel can be computed independently, enabling embarrassingly parallel computation. We show that alternating between convex optimization and parallel grid search can effectively solve the depth-from-defocus problem at higher resolutions than current deep learning methods. We demonstrate our approach on benchmark datasets with synthetic and real defocus blur and show promising results compared to prior approaches. Our code is available at github.com/hollyjackson/dfd.

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.

Image reconstruction from corrupted images is crucial across many domains. Most reconstruction networks are trained on post-ISP sRGB images, even though the image-signal-processing pipeline irreversibly mixes colors, clips dynamic range, and blurs fine detail. This paper uses the rain degradation problem as a use case to show that these losses are avoidable, and demonstrates that learning directly on raw Bayer mosaics yields superior reconstructions. To substantiate the claim, we (i) evaluate post-ISP and Bayer reconstruction pipelines, (ii) curate Raw-Rain, the first public benchmark of real rainy scenes captured in both 12-bit Bayer and bit-depth-matched sRGB, and (iii) introduce Information Conservation Score (ICS), a color-invariant metric that aligns more closely with human opinion than PSNR or SSIM. On the test split, our raw-domain model improves sRGB results by up to +0.99 dB PSNR and +1.2% ICS, while running faster with half of the GFLOPs. The results advocate an ISP-last paradigm for low-level vision and open the door to end-to-end learnable camera pipelines.

Humans learn in two complementary ways: a slow, cumulative process that builds broad, general knowledge, and a fast, on-the-fly process that captures specific experiences. Existing deep-unfolding methods for spectral compressive imaging (SCI) mirror only the slow component-relying on heavy pre-training with many unfolding stages-yet they lack the rapid adaptation needed to handle new optical configurations. As a result, they falter on out-of-distribution cameras, especially in bespoke spectral setups unseen during training. This depth also incurs heavy computation and slow inference. To bridge this gap, we introduce SlowFast-SCI, a dual-speed framework seamlessly integrated into any deep unfolding network beyond SCI systems. During slow learning, we pre-train or reuse a priors-based backbone and distill it via imaging guidance into a compact fast-unfolding model. In the fast learning stage, lightweight adaptation modules are embedded within each stage and fine-turned self-supervised at test time via a self-supervised loss-without retraining the backbone. To the best of our knowledge, SlowFast-SCI is the first testtime adaptation-driven deep unfolding framework for efficient, self-adaptive spectral reconstruction. Its dual-stage design unites offline robustness with on-the-fly per-sample calibration-yielding over 70% reduction in parameters and FLOPs, up to 5.79 dB PSNR improvement on out-of-distribution data, preserved cross-domain adaptability, and a 4x faster adaptation speed. In addition, its modularity integrates with any deep-unfolding network, paving the way for self-adaptive, field-deployable imaging and expanded computational imaging modalities. Code is available in Supplementary Material. The models, datasets, and code are available at https://github.com/XuanLu11/SlowFast-SCI.

In this work, we propose Fast Equivariant Imaging (FEI), a novel unsupervised learning framework to rapidly and efficiently train deep imaging networks without ground-truth data. FEI reformulates the EI objective through an inexact variable-splitting scheme, decoupling network training from an auxiliary restoration step implemented with a plug-and-play denoiser, this novel unsupervised scheme shows superior efficiency and performance compared to the standard Equivariant Imaging paradigm. In particular, our FEI schemes achieve an order-of-magnitude (10x) acceleration over standard EI on training U-Net for X-ray CT reconstruction and image inpainting, with improved generalization performance. Beyond offline training, the proposed scheme also enables efficient test-time adaptation of a pretrained model to individual samples, to secure further performance improvements. Extensive experiments show that the proposed approach provides a noticeable efficiency and performance gain over existing unsupervised methods and model adaptation techniques.