Image Inverse Problems

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10 papers in the last four weeks, up 150% on the four weeks before. 0.1% of all new papers.

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Latest papers 85

Oct 7, 2026cs.LG

Self-attention summary networks for subsurface velocity-model building from common-image gathers

Common-image gathers (CIGs) contain physically meaningful information about velocity-model errors through reflector focusing and residual moveout, but in conventional imaging workflows they are typically used only as diagnostic tools. In this work, we propose a multiscale self-attention summary network that maps high-dimensional 3D CIG volumes into compact conditioning embeddings for probabilistic subsurface velocity inversion. These learned embeddings preserve offset-dependent kinematic structure and spatial coherence while reducing variability caused by background-velocity mismatch. Conditioned on these summary embeddings, a flow-matching model learns a transport from a Gaussian source distribution to the posterior distribution of plausible velocity fields. Numerical experiments show that, compared with direct conditioning on raw CIGs, the proposed summary network improves posterior velocity inference. In particular, the multiscale attention design provides greater robustness to background-model mismatch, yielding more accurate posterior reconstructions and lower predictive uncertainty.

Shiqin Zeng, Yunlin Zeng, Abhinav Prakash Gahlot +2

Georgia Institute of Technology

Inverse Problems Bayesian Inverse Problems Image Inverse Problems Multi-Scale Attention

Oct 7, 2026cs.LG

Twist Flow for Inverse Problems

In Bayesian inverse problems, posterior sampling requires generating samples that are consistent with given observations while capturing the range of plausible solutions. Direct conditional generative models introduce latent noise to model this ambiguity, but paired inverse-problem training can still encourage an almost deterministic map from the observation to the target. As a result, generated samples may be observation-consistent while under-representing posterior variability, especially when the posterior is multimodal, leading to undercoverage, mode distortion, or artificial transitions between distinct feasible solutions. We propose joint twist-flow, an augmented flow-matching formulation that learns a continuous transport from the augmented source state

(z_x, y)

to the augmented terminal state

(x, z_y)

. Here x is the target variable,

y

is the observation,

z_x

is the Gaussian reference coordinate for posterior sampling, and

z_y

is a Gaussian likelihood-side coordinate associated with the observation branch. Under a Gaussian observation model,

z_y

is motivated by the normalized observation residual associated with observation compatibility. Its role is not to replace uncertainty in

x

, but to couple generated samples of x to observation consistency, helping reduce likelihood-inconsistent variation while preserving variability in weakly constrained directions. We validate the method on low-dimensional inverse problems with reference posterior samples, where joint twist-flow better preserves multimodal posterior support than a direct conditional-flow baseline. We further evaluate the method on image restoration and seismic subsurface velocity-model inversion, showing increased posterior variability while maintaining observation consistency.

Shiqin Zeng, Zijun Deng, Felix J. Herrmann

Georgia Institute of Technology

Bayesian Inverse Problems Posterior Sampling Inverse Problems Flow Matching Image Inverse Problems

Oct 6, 2026cs.GR

UltraDiff: Differentiable Ray Tracing in Ultrasound for Shape Optimization

Physically-based differentiable rendering enables gradient-based optimization of scene parameters by matching rendered images to measurements, but has so far mainly focused on light transport. We extend this paradigm to medical ultrasound, where image formation resembles transient rendering: echoes are binned by time-of-flight rather than projected onto an image plane. We present UltraDiff, a modular framework for differentiable ultrasound ray tracing. UltraDiff formulates ultrasound image formation as a path-space integral, gated by travel time between the transducer and tissue interfaces, and derives a Monte Carlo estimator of both the forward model and its gradients with respect to scene parameters. We demonstrate this on an inverse geometry estimation: starting from a sphere, an SDF is optimized until simulated echoes match measured ones, recovering vertebral surfaces from simulated B-mode sweeps and from a real robotic acquisition of a spine phantom. Unlike state-of-the-art ultrasound shape reconstruction methods, which rely on pre-segmented images, our approach operates unsupervised on B-mode images through analysis-by-synthesis, while achieving competitive geometric accuracy. Implemented on top of Mitsuba 3, UltraDiff brings differentiable path tracing to a new sensing modality and provides a foundation for inverse problems in acoustic imaging.

Felix Duelmer, Magdalena Wysocki, Nassir Navab +1

Technical University of Munich & Munich Center for Machine Learning

Differentiable Rendering Ultrasound Imaging Image Inverse Problems

Sep 29, 2026cs.CV

Principled MAP estimation for inverse problems: bridging the gap between convergence and performance

Pretrained denoisers provide a powerful way to incorporate image priors into restoration algorithms. Plug-and-Play and RED approaches exploit fixed-noise-level denoisers within first-order optimization schemes, with convergence guarantees, but often struggle to achieve high-quality reconstruction on severely ill-posed inverse problems. In contrast, recent state-of-the-art approaches leverage denoisers derived from flow- or diffusion-based generative models and evaluate them along a sequence of decreasing noise levels. While these methods achieve strong empirical performance, their convergence theory remains limited. In this paper, we bridge this gap by specifically designing an algorithm that combines denoisers at decreasing noise levels with a schedule tailored to ensure convergence. From a Bayesian perspective, we prove that our method converges to a

\textit{Maximum a Posteriori}

(MAP) estimate, under suitable assumptions. Subsequently, we apply our method to various ill-posed inverse problems and show that it surpasses convergent methods while competing with state-of-the-art empirical ones.

Alexandre Lagier, Valentine Tosel, Anne Gagneux +2

ENS de Lyon, CNRS, Université Claude Bernard Lyon 1, Inria, LIP UMR 5668, 69342 Lyon Cedex 07, France · Univ. Bordeaux, Inria, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France · Inria, ENS de Lyon, CNRS, Université Claude Bernard Lyon 1, LIP UMR 5668, 69342 Lyon Cedex 07, France

Bayesian Inverse Problems Bayesian Inference Image Restoration Diffusion-Based Inverse Problems Image Inverse Problems

Sep 28, 2026cs.LG

Livin' on a Prior: Likelihood Score Approximation for Inverse Problems

Generative models have found great success as data-driven methods of solving inverse problems. Two popular approaches work either by combining a pretrained generative prior with a known degradation model, or by training a conditional generative model directly from paired data. We target a setting that spans both regimes: unknown degradations can be learned from few paired examples, while known degradations can be learned from self-generated samples. We introduce Likelihood Score Approximation (LSA), a generative framework that keeps a pretrained unconditional model fixed and learns an observation-conditioned model that approximates the likelihood score from paired samples. Within a conditional stochastic-interpolant framework, LSA can be trained in either score or velocity coordinates, independently of the unconditional model's native parameterization, and supports both deterministic and stochastic sampling. We further show empirically that the prior model can be swapped post-training while keeping the same LSA model. Across speech and image inverse problems, LSA operates effectively even at roughly 0.01% of the full training dataset. On the ImageNet-256 benchmark it achieves competitive or better restoration quality than strong posterior-sampling baselines while requiring up to several orders of magnitude fewer network evaluations.

Rostislav Makarov, Tal Peer, Danilo de Oliveira +1

Signal Processing University of Hamburg Hamburg, Germany

Conditional Generative Modeling Inverse Problems Image Inverse Problems

Sep 26, 2026math.OC

Convergent Plug-and-Play Image Restoration with Annealed Noise Levels

Plug-and-Play (PnP) methods solve imaging inverse problems by incorporating deep denoisers into iterative optimization algorithms. Although practical implementations often decrease the denoiser noise level

σ

along iterations, most existing convergence analyses assume a fixed denoiser. In this work, we establish convergence guarantees for a broad family of Plug-and-Play algorithms with annealed noise level, spanning deterministic methods (RED--GD and PnP--PGD) and stochastic methods (SNORE, equivariant RED, and a variant of PnP--Flow). For each method, we identify an explicit, nonconvex objective associated with the terminal denoising level and prove asymptotic stationarity of the iterates with respect to this objective. Our analysis does not prescribe any decay rate for the noise schedule, and our assumptions cover both learned gradient-step denoisers and exact MMSE denoisers. Overall, our theoretical results bridge the gap between existing PnP convergence theory and the decreasing-denoising practices used by state-of-the-art image restoration methods. We empirically demonstrate the benefits of such schedules and illustrate the predicted convergence behavior on several imaging inverse problems, including inpainting, super-resolution, demosaicing and tomography.

Samuel Hurault

LIGM, CNRS, Univ. Gustave Eiffel

Convergence Analysis Image Restoration Image Inverse Problems

Sep 20, 2026cs.CV

Compact Low-Cost Hyperspectral Imaging via Angular-to-Spectral Diversity Conversion

Snapshot hyperspectral imaging avoids sequential scanning, but systems that jointly achieve stable reconstruction, low cost, and compact optics remain limited. We present a snapshot hyperspectral imaging system based on angular-to-spectral diversity conversion. A tapered kaleidoscope creates replicated views with distinct incidence directions, and a directly attached birefringent filter converts them into view-channel-dependent spectral transmittances, yielding complementary measurements that better condition the inverse problem for more stable single-shot spectral reconstruction. The system preserves a simple pixel-wise linear model for fast non-learning-based reconstruction and uses only off-the-shelf components without relay optics or cascaded modules. We select the birefringent filter configuration using a condition-number-based criterion and validate the system on both synthetic and real data.

Kazuma Fujiwara, Takuya Funatomi, Kazuya Kitano +2

Nara Institute of Science and Technology, Nara, Japan · Kyoto University, Kyoto, Japan

Hyperspectral Imaging Computational Imaging Image Inverse Problems

Sep 17, 2026cs.CV

FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolants

Flow matching has emerged as the state-of-the-art generative model and has been used for plug-and-play (PnP) priors to solve inverse problems in computational imaging. However, existing flow-based inverse solvers assume linear forward models and/or make simplifying approximations in posterior sampling. To circumvent these problems, we introduce FlowSGS, a flow-based posterior sampling method using Split Gibbs Sampling (SGS) to decompose the posterior into a likelihood step and a prior step. Specifically, we sample from the likelihood step using Langevin dynamics and leverage the Stochastic Interpolants (SI) framework to integrate a pretrained flow model into the prior step. We provide a form for the prior step that uses SI's reverse-time SDE, and show connections to previous PnP methods. Moreover, with the aid of the flow prior's straight probability paths and a novel timestep correction technique for the reverse-time SDE, FlowSGS requires fewer network evaluations in its prior step than plug-and-play diffusion samplers. Our experiments show state-of-the-art performance on a range of inverse problems. For the first time, we provide an experiment on a nonlinear inverse problem (Fourier phase retrieval) for flow-based inverse solvers.

Tianao Li, Xinhui Qian, Emma Alexander

Department of Computer Science, Northwestern University · NSF-Simons AI Institute for the Sky (SkAI) · Department of Statistics and Data Science, Northwestern University

Flow Matching Markov Chain Monte Carlo Posterior Sampling Flow-Based Generative Modeling Image Inverse Problems

Sep 17, 2026cs.LG

Learning-Based Reconstruction of Optical Properties in Bilayered Media from Single-distance Time-Resolved Reflectance Measurements

The inverse problem of reconstructing optical properties, specifically absorption and scattering coefficients, in layered biological media from time-domain reflectance measurements remains a significant challenge for traditional analytical models. Inverse solvers based on the diffusion equation often struggle with structural heterogeneity, frequently yielding poor accuracy for superficial absorption and deep-layers scattering. In this work, we propose a machine learning framework as an alternative approach to reconstruct the optical properties of a bilayered medium, benchmarking its efficiency and accuracy against model-based algorithms. To overcome the intrinsic approximations of diffusion theory and inverse reconstruction, we generated a robust synthetic dataset of forward DTOF using exact Monte Carlo simulations at multiple source-detector distances. A machine learning pipeline was then trained on this dataset and validated against state-of-the-art model-based reconstruction methods. Besides the significant reconstruction speed-up, the machine learning approach achieves higher accuracy than model-based inverse solvers, further providing an estimate of the parameter space dimensionality without requiring any a priori information about the number of layers in the investigated geometry. Further enhancements in the reconstruction accuracy can be expected in future extensions of this work, by training the pipeline over multiple DTOF curves from the same medium, in a joint multi-distance reconstruction approach.

Caterina Amendola, Giulia Maffeis, Lorenzo Buffoni +8

Department of Physics, Politecnico di Milano, Milan, 20133, Italy

Inverse Problems Image Inverse Problems

Sep 17, 2026cs.CV

STAR: Structure-aware Test-time Adaptation for diffusion-based light field Reconstruction

Light field (LF) reconstruction from limited and noisy focal stack (FS) measurements is a highly ill-posed inverse problem. Although the LF-to-FS imaging geometry is fixed for a given optical setup, LF spatial-angular structure---including within-view spatial details, cross-view angular dependencies, and disparity across views---varies across scenes. Consequently, a fixed pre-trained prior may not optimally capture the spatial-angular structure of each test LF. We propose Structure-aware Test-time Adaptation for diffusion-based light field Reconstruction (STAR), the first test-time adaptation framework for reconstructing an LF from FS. For each test LF, STAR freezes a pre-trained diffusion prior and fits three lightweight adapters to the observed FS to jointly adapt the three components of the LF's spatial-angular structure. STAR outperforms existing state-of-the-art methods in both two- and three-focal-sheet settings, with shorter inference times than those with test-time parameter updates.

Wontae Choi, Ki Ryum Moon, Jae Young Lee +2

Department of Artificial Intelligence (AI), Sungkyunkwan University (SKKU), Suwon, South Korea · Department of Electrical and Computer Engineering, SKKU, Suwon, South Korea

Image Reconstruction Computational Imaging Diffusion-Based Inverse Problems Diffusion Models Image Inverse Problems

Sep 14, 2026cs.LG

Backward SDEs-based Diffusion for Physics-Constrained Generation

Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is often handled by heuristic guidance, intermittent projections, or task-specific conditional training, with limited guarantees of feasibility at the end of inference. We propose terminal-conditioned inversion for score-based SDE priors. Given a frozen Score-SDE prior and a task-defined terminal feasibility specification, we construct an associated backward stochastic differential equation whose adapted solution defines a principled inverse map from the terminal requirement to a prior state at a chosen noise level. Under standard regularity conditions, we establish existence and uniqueness of the adapted solution and obtain terminal consistency by construction. We further develop a practical neural BSDE solver that composes arbitrary pretrained diffusion priors with domain constraints without modifying the score-defined coefficients, producing an anchored prior state that enables neighborhood sampling for uncertainty characterization. Experiments on toy datasets validate stable terminal-conditioned inversion and distributionally consistent neighborhood sampling. As a real-world case study, we apply the framework to sparse-view CT reconstruction and achieve improved reconstruction quality over representative training-free baselines while satisfying strict measurement feasibility under the prescribed terminal specification. Project is available in: https://laplace.center/icmlbsdeI/

Zihao Wang

Diffusion Model Inversion Constrained Generative Modeling Stochastic Differential Equations Diffusion-Based Inverse Problems Image Inverse Problems

Sep 14, 2026cs.LG

Physical-State-Guided Diffusion Sampling for Full-Waveform Inversion

Full waveform inversion (FWI) estimates subsurface velocity from seismic recordings, but its ill-posedness and nonlinearity make accurate reconstruction strongly dependent on initialization and prior information. Diffusion posterior sampling provides a learned geological prior, yet directly coupling its denoiser to the nonlinear wave solver can yield unreliable physical guidance. We propose Physical-State-Guided Diffusion Sampling (PSG), which couples a persistent physical velocity to the diffusion prior through a Gaussian bridge. The physical state is refined by waveform fitting regularized by the denoised velocity, and in turn guides the reverse diffusion process. This formulation separates the wave-equation and denoiser gradients while preserving conventional FWI initialization and accumulated optimization history. On four OpenFWI families, PSG's terminal denoised estimates outperform classical and diffusion-based baselines under clean and missing-trace acquisitions and maintain strong structural recovery under measurement noise. Repeated stochastic runs preserve the dominant geological structures, with ensemble variability concentrated near geological interfaces and positively associated with local inversion error. A frozen OpenFWI-trained prior further supports inversion of the larger Marmousi, Overthrust, and BP2004 Salt models, recovering complex geological structures without retraining.

Chen Min, Haowen Jiang, Zheng Ma +1

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China · CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, China · School of Mathematics and Statistics, Lanzhou University, Lanzhou, China

Physics-Informed Diffusion Models Diffusion-Based Inverse Problems Diffusion Posterior Sampling PDE Inverse Problems Inverse Problems Image Inverse Problems

Sep 11, 2026cs.CV

FIRM: Flow-based Imaging via Regularized Minimization

Flow matching methods for imaging inverse problems typically incorporate measurements through network conditioning or guidance during sampling. Neither approach explicitly applies the forward operator within the learned conditional velocity field. We develop a principled measurement-conditional velocity parameterization that does. For a linear interpolation path, we express the optimal velocity through the posterior mean

E[x_1|x_t, y]

and show that this mean is the unique minimizer of a variational objective with an explicit data-consistency term. The velocity defined by this minimizer provably transports the source distribution to the measurement-conditioned posterior. This result leads to a forward operator-aware velocity field that is trained end-to-end and requires no separate guidance during sampling. Across five imaging tasks, our method achieves leading reconstruction quality with up to

50\times

fewer network evaluations than competitive flow-based methods. Varying the number of sampling steps also controls the distortion-perception trade-off without retraining.

Shirin Shoushtari, Edward P. Chandler, Xiao Shi +1

WashU · UW-Madison

Conditional Flow Matching Image Reconstruction Inverse Problems Image Inverse Problems

Sep 1, 2026cs.CV

Diffusion Based Unpaired Data Learning for Inverse Problems

Data is important in many deep learning-based inverse problem solvers. However, obtaining sufficient paired data in many scenarios remains highly challenging, while unpaired data is cheap. To maximize data utilization, this paper proposes LUD-DIF, a diffusion-based approach for solving inverse problems with unpaired data. Starting from the evidence lower bound (ELBO) of the joint distribution, we decouple it into two independent diffusion processes under the weak-coupling assumption. The method provides theoretical support from a variational inference perspective, derives the loss function, quantitatively analyzes the error bound introduced by the assumption, and offers a theorem-motivated heuristic for hyperparameter selection. Experimental results demonstrate that LUD-DIF achieves outstanding performance on multiple image inverse problems, validating its effectiveness and generalization capability in unpaired inverse problem settings.

Chenglong Bao, Yiming Dang, Chenguang Duan +2

Yau Mathematical Sciences Center, Tsinghua University, Beijing, China · Department of Mathematical Sciences, Tsinghua University, Beijing, China · Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany +2

Diffusion-Based Inverse Problems Inverse Problems Diffusion Models Image Inverse Problems

Sep 1, 2026cs.CV

ReBridge-Flow: Re-Coupling Posterior Bridges in Flow Matching for Image Restoration

Flow Matching provides an efficient generative prior for image restoration by learning continuous transport between source and data distributions. However, existing methods typically incorporate measurement constraints through local corrections. Such corrections may disrupt the source-clean endpoint coupling implicitly encoded by the pretrained flow, making the corrected endpoint pair incompatible with the current state. To address this issue, we propose ReBridge-Flow, a posterior bridge re-coupling method. Specifically, given the current state, ReBridge-Flow first decodes the corresponding local source and clean endpoints. It then incorporates measurement information through clean-side anchoring and synchronously re-couples the source endpoint, yielding a measurement-aware endpoint pair with improved local bridge compatibility. The re-coupled endpoints further define a posterior-informed transport direction for advancing the sampling process. We also introduce the Posterior Bridge Defect, which jointly characterizes measurement error, deviation from the flow prior, and bridge mismatch, and leads to explicit updates for clean-side anchoring and source-side re-coupling. Extensive experiments on multiple natural and medical image restoration tasks demonstrate that ReBridge-Flow effectively alleviates bridge mismatch and improves the structural consistency of restored images.

Jiaqi Zhang, Yiqi Wang, Hongjie Wu +6

Jiangsu University · Griffith University · Sichuan University +5

Image Restoration Image Inverse Problems

Aug 15, 2026stat.ML

A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors

Pretrained diffusion models represent image distributions through a continuum of progressively smoothed distributions. This multiscale structure organizes generation from global structure to fine detail and supports high-quality, diverse samples. We exploit the same multiscale diffusion prior for linear imaging inverse problems. Rather than using the pretrained model only as a denoiser in an outer iteration, we define a surrogate likelihood whose center is aligned with the clean-image coordinate and whose covariance accounts for residual diffusion uncertainty. This construction defines an explicit surrogate posterior path, from which we derive continuous posterior dynamics. A tunable Langevin component supports target tracking and allows the amount of posterior exploration to be adapted to the application. We prove endpoint consistency and a finite-horizon tracking bound and, in the exact-score setting, first-order weak accuracy. For computation, we derive the Posterior-Dynamics Implicit--Explicit sampler (PD-IMEX), a stable method using one score evaluation per diffusion scale and an implicit data-consistency update. Experiments on deblurring, super-resolution, and inpainting show strong reconstruction quality at 100 score evaluations, coarse-grid stability, and controllable fidelity--diversity behavior.

Zhaoqiang Liu, Tongyao Pang, Ruibing Wang +1

School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China · Yau Mathematical Sciences Center, Shuangqing Complex, Tsinghua University, Beijing 100084, China

Diffusion Models for Image Restoration Bayesian Inverse Problems Diffusion-Based Inverse Problems Diffusion Posterior Sampling Image Inverse Problems

Aug 12, 2026cs.CV

Making Every Step Count: Spatio-Temporal Information Allocation for Imaging Inverse Problems

Flow-based generative models have emerged as powerful image priors for training-free inverse problem solving, capturing coherent semantics and fine-grained structure. Despite these strengths, existing flow-based inverse solvers primarily focus on the design of individual updates, largely overlooking spatio-temporal information allocation under a fixed number of function evaluations (NFEs). Temporally, insufficient early exploration can trap the flow trajectory in an incorrect semantic basin, whereas excessive allocation of NFEs to early stages leaves little budget for late-stage refinement. Spatially, data consistency provides direct constraints only within observed regions, whereas the recovery of missing regions relies mainly on the generative prior. To address these two issues, we introduce two complementary and training-free components, i.e., Spectrum-Adaptive Scheduling (SAS) and Measurement-Prioritized Attention (MPA). For temporal allocation, SAS distributes the available NFEs over flow time according to the degradation spectrum and logSNR geometry, thus better balancing semantic exploration and detail refinement. For spatial propagation, MPA exploits data-prior conflicts to guide information toward weakly constrained regions, thereby enhancing semantic and structural fidelity. Extensive experiments on standard image inverse problems, e.g., super-resolution, motion deblurring, and inpainting, demonstrate that the proposed components can be integrated into existing flow-based inverse solvers in a plug-and-play manner without retraining or additional flow-model evaluations, and can also significantly improve the restoration quality of existing solvers.

Yi Cao, Xiangyong Cao, Pei Liu +2

Xi’an Jiaotong University · Tsinghua University

Inference-Time Optimization Image Restoration Flow-Based Generative Modeling Image Inverse Problems

Aug 6, 2026math.NA

A neural operator view on U-Nets for inverse imaging problems

Deep neural networks have shown great empirical success in the solution of a wide variety of ill-posed inverse problems in imaging. Yet, very few works have studied their behavior in the limit that turns the discretized ill-conditioned problems into truly ill-posed ones, i.e., for an increasing resolution of the discretization. In this work, we review common approaches to neural operator learning in architectures that resemble a U-Net, one of the most common classical architectures for inverse imaging problems. We discuss advantages and drawbacks of the respective approaches, consider a 1D toy example for improved interpretability, and present extensive numerical experiments on how different types of neural operator U-Nets can improve a first (crude) limited angle CT-reconstruction. In particular, we study how well networks trained for a certain resolution of the discretization generalize to other resolutions. Our finding is that while U-shaped neural operator architectures are by design resolution-invariant, the classical U-Net architecture seems to be more robust with respect to resolution changes than expected.

Alexander Auras, Martin Burger, Samira Kabri +2

Computer Vision Group, University of Siegen, Hölderlinstraße 3, 57076 Siegen, Germany · Helmholtz Imaging, Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, Hamburg, 22607, Germany · Fachbereich Mathematik, Universität Hamburg, Bundesstrasse 55, Hamburg, 20146, Germany

U-Net Neural Operators Image Inverse Problems

Aug 1, 2026cs.CV

Hybrid-Domain Posterior Sampling for Inverse Problems via Latent Flow Matching

Latent Flow Models have revolutionized compressed-space image synthesis, yet their application to high-fidelity inverse problems remains bottlenecked. In this paper, we trace this dilemma to a fundamental geometric limitation of pre-trained autoencoders, which we term \emph{First-Order Manifold Blindness}. Severe decoder compression (e.g., retaining only

\sim\!2\%

of the original degrees of freedom) produces a rank-deficient Jacobian, rendering high-frequency measurement residuals in its orthogonal complement invisible to latent gradients even when the decoder can represent the target image. To overcome this bottleneck, we propose Hybrid-Domain Posterior Sampling (HDPS), a decoupled inference framework that disentangles physical measurement consistency from semantic prior modeling. HDPS diverges into the pixel space, leveraging Langevin dynamics to absorb precise orthogonal measurement gradients, and subsequently projects these structural corrections back onto the generative manifold. An optimization-based latent alignment is introduced to filter pixel-space artifacts while avoiding the semantic drift of direct encoding. Extensive experiments on diverse inverse problems demonstrate that HDPS establishes a new state-of-the-art, successfully recovering the high-frequency structural precision that latent-only solvers inherently discard. The code is available at https://github.com/74587887/HDPS.

Hongjie Wu, Yiping Xie, Jiancheng Lv

College of Computer Science, Sichuan University Chengdu, China

Bayesian Inverse Problems Image Inverse Problems

Jul 25, 2026eess.IV

Trainable Nonexpansive Denoisers for Contractive Image Reconstruction

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.

Arghya Sinha, Aditya Banerjee, Trishit Mukherjee +1

Indian Institute of Science, Bengaluru, India.

Image Reconstruction Lipschitz Neural Networks Image Inverse Problems Image Denoising

Jul 25, 2026eess.IV

Stabilizing Deep Reconstruction Operators with Contractive Anchoring

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.

Arghya Sinha, Trishit Mukherjee, Kunal N. Chaudhury

Indian Institute of Science, Bengalore, India

Algorithmic Stability Image Reconstruction Image Inverse Problems

Jul 24, 2026cs.LG

IQ-JEPA: A Joint-Embedding Predictive Architecture with a Hermitian Vision Transformer for Sound Speed and Attenuation Estimation from Ultrasound IQ Data

The speed of sound in tissue is a prerequisite for well-focused imaging and has diagnostic value, but recovering it from raw pulse-echo channel data is fundamentally a nonlinear inverse problem. Learned solvers are fast yet label hungry. Simulated sound-speed labels are expensive, while abundant real channel data is unlabeled. We propose IQ-JEPA to exploit both data types. An encoder is pretrained without labels to predict the latent representation of masked in-phase and quadrature (IQ) regions from visible context, then fine-tuned on simulated maps. Sound speed appears in the IQ signal as a phase difference, invariant to the constant phase offset. The encoder is a Hermitian vision transformer that operates on the complex signal directly. Its attention is equivariant to that phase and its conjugate-product feed-forward is invariant to it, so the encoder reads a quantity analogous to the one classical coherence methods use. On 79,293 Fullwave 2.5 simulations at 2.5 MHz, pretraining on the 63,435 unlabeled acquisitions reaches 15.60 m/s at 10,000 labels. This is a roughly threefold gain in label efficiency over supervised training, growing to over fourfold at 1,000 labels. It is about 2.2x below an InversionNet baseline, and 8.71 m/s at full labels. The gain still grows with more unlabeled pretraining data. Our comparisons point to self-supervision as the dominant factor. The same encoder transfers. Its frozen features expose sound speed and attenuation, and cross-distribution pretraining between layered and abdominal phantoms costs little accuracy. We see this as a first step toward a foundation model for quantitative ultrasound.

Masashi Sode, Gianmarco Pinton

Joint Department of Biomedical Engineering, University of North Carolina at Chapel Hill and North Carolina State University, Chapel Hill, NC 27599 USA

Self-Supervised Pre-Training Joint-Embedding Predictive Architecture Complex-Valued Neural Networks Ultrasound Imaging Image Inverse Problems

Jul 16, 2026eess.IV

ESAR: Event-Based Synthetic Aperture Reconstruction

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.

Harbir Antil, Daniel Blauvelt, David Sayre

Event-Based Vision Computational Imaging Image Inverse Problems

Jul 14, 2026eess.IV

Efficient Computing for Medical Image Acquisition and Reconstruction

Medical imaging systems such as CT, MRI, PET, and SPECT do not directly acquire images. Instead, they measure physical signals that encode anatomical or physiological information, and image reconstruction recovers the underlying image by solving an inverse problem. Although these imaging modalities are governed by different imaging physics, they share a common computational framework that naturally connects medical physics, linear algebra, probability, numerical optimization, and efficient computing. As medical imaging systems acquire increasingly large and higher-dimensional datasets, image reconstruction has become one of the primary computational bottlenecks in modern medical imaging. Advanced reconstruction methods, including analytical reconstruction, iterative optimization, and statistical model-based reconstruction, substantially improve image quality while reducing radiation dose or scan time, but at significantly increased computational cost. Efficient computing has therefore become essential for achieving clinically practical reconstruction times. This chapter presents a unified computational perspective on medical image acquisition and reconstruction across CT, MRI, PET, and SPECT. It first reviews the imaging physics and data acquisition process for each modality and derives a generalized mathematical framework for image reconstruction. Building on this framework, the chapter discusses analytical, iterative, and statistical reconstruction methods together with their computational characteristics. Finally, it examines efficient computing considerations, including optimization algorithms, physics-aware forward operators, memory-efficient implementations, and parallel computing strategies. Together, these topics demonstrate how the integration of imaging physics, mathematical modeling, and efficient computing enables accurate and scalable medical image reconstruction.

Xiao Wang, Jayasai Rajagopal, Md Safaiat Hossain +4

Medical Imaging Image Reconstruction Computational Imaging Image Inverse Problems

Jul 14, 2026cs.LG

From Preimage Search To Source-Grounded Feature Inversion

Interpreting a neural network requires understanding what its internal features extract from a particular input. Feature inversion seeks to express a selected feature in the input domain, but canonical iterative methods search for an input whose re-encoded representation matches the target. Because many inputs can satisfy this constraint, target matching alone does not specify the inverse associated with the sample that generated the feature. We formulate source-grounded feature inversion by conditioning the inverse on the source-local network geometry at the target-generating input. At each boundary of the computational DAG, backpropagation provides the correct reverse dependencies but transports an adjoint signal rather than an upstream-state estimate. We locally repair this signal with a closed-form matrix Wiener map from a mean-seed VJP to the upstream state, followed by a second Wiener map for the JVP forward-consistency residual, and compose the repaired states through the same DAG in one finite reverse pass. One calibrated zero-intercept map family supports new inputs, depths, channels, and channel groups across diverse CNN and Transformer architectures, tensor components, and visual distributions without query-specific optimisation. Matched target and source controls verify that each inverse depends on the selected feature and the local operators of the sample being explained, rather than a target-independent image template. Prediction-conditioned feature atlases align these visualisations with independent interventions on the corresponding internal features. Together, source-grounded feature inversion opens the model's hidden feature hierarchy to inspection at the level of individual layers and channels, linking what the network extracts from an input to the internal evidence that shapes its decision.

Kaixiang Shu

Independent Researcher

Neural Network Interpretability Image Inverse Problems

Jul 12, 2026cs.AI

Imaging-101: Benchmarking LLM Coding Agents on Scientific Computational Imaging

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.

Siyi Chen, Jiahe Ying, Yixuan Jia +9

Key Laboratory of Spacecraft Design Optimization and Dynamic Simulation Technologies, Ministry of Education, Beijing, 102206, China

AI Agents for Scientific Discovery Computational Imaging LLM Agents Image Inverse Problems

Jul 3, 2026cs.LG

Mixture-of-Gaussians-Guided Schedule Design for Brownian Bridge Diffusion Models

Brownian Bridge Diffusion Models (BBDM) offer an appealing framework for image restoration and inverse problems by constructing a stochastic bridge from the clean signal directly to the degraded observation, rather than to pure noise. Despite their promise, the choice of bridge schedule is typically inherited from heuristics, and a principled analytical framework for schedule design has been lacking. In this work, we develop such a framework by offering a novel analysis of BBDM reverse dynamics under a Mixture-of-Gaussians (MoG) prior. This setting yields a closed-form ideal posterior and a corresponding MMSE denoiser, while the BBDM-induced reconstruction law is captured analytically through a tractable surrogate. Building on these expressions, we formulate two complementary schedule-design objectives: a Wasserstein criterion targeting perceptual quality and an MSE criterion targeting reconstruction fidelity. Our work exposes an inherent tradeoff between the two and proves the existence of universal schedules for both that are independent of the degradation and prior. Extensive experiments on controlled MoG settings confirm full alignment between theory and practice, and experiments on the FFHQ dataset across inpainting, deblurring, and super-resolution tasks validate the practical value of our schedule-design criteria.

Ron Levi, Michael Elad

Department of Computer Science Technion, Israel

Diffusion Models for Image Restoration Diffusion-Based Inverse Problems Diffusion Models Image Inverse Problems

Jul 1, 2026cs.CV

High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstruction

Magnetic resonance imaging (MRI) reconstruction under realistic acquisition conditions can be fundamentally viewed as estimating the underlying k-space distribution from incomplete and noise-corrupted measurements. While diffusion models have recently shown strong potential as generative prior for inverse problems,existingapproachesstruggletohandlenoisyreconstruction settings, especially when operating directly in k-space domain. In this work, we propose a unified high-dimensional k-space reconstruction framework tailored for noisy inverse problems, whichenhancesdiffusion-based solversthroughrepresentation lifting.Ratherthanmodifyingthe underlying optimization procedures, the proposed framework augments the data representation space, enabling existing diffusion-based solvers to operate on enriched k-space embeddings with improved expressiveness. Extensive experiments on both in-house and public datasets across varying noise levels and undersampled factors demonstrate that the proposed frame work consistently improves reconstruction quality for multiple diffusion-based inverse solvers. Notably, the largest gains are observed in high-noise regimes, which is consistent with our theoretical analysis of error propagation under high-dimensional representation. These results suggest that high-dimensional representation provides a general and model-agnostic mechanism for improving diffusion-based MRI reconstruction in noisy settings, offering a new perspective on robust k-space generative modeling for practical inverse problems. The code will be available at https://github.com/yqx7150/HEP-MRIRec.

Yu Guan, Tianjia Huang, Qinrong Cai +3

Diffusion Models for Image Restoration Accelerated MRI Reconstruction Diffusion-Based Inverse Problems Diffusion MRI Diffusion Models Image Inverse Problems

Jul 1, 2026cs.CV

Radial Interaction Tomography: Recognizing Non-Transitive Evolutionary Games from One Range-Expansion Image

Colored sectors in a microbial range expansion encode more than lineage survival counts. We formulate a computer-vision inverse problem: from one endpoint image of an accretive multi-type expansion, recover the radius-indexed pairwise boundary-flow field and test whether the visual pattern is compatible with a transitive scalar fitness hierarchy. The observable is a geometric signal extracted from sector-boundary curves in log-polar coordinates. We prove endpoint observability and stability for frozen fronts, weighted transitive/cyclic decomposition, contact-complete circular design, physical-clock and mechanism non-identifiability, exact Gaussian cyclicity testing, and Bonferroni-valid interval scanning. The benchmark is deterministic: analytic endpoint images, blurred/noisy pixel round trips, scalar-null stress tests, public-image tracing, multi-resolution mechanistic endpoints, and a non-learning frozen-front simulator. The implementation recovers pairwise edge-flow histories from endpoint images, detects cyclic residuals in a mechanistic four-type expansion, and uses those residuals as forcing signals for a dimensionless active design-control layer covering reaction-diffusion control, phenotype-frontier optimization, protocol synthesis, Monte Carlo robustness, and a downstream population-state bridge.

Faruk Alpay, Baris Basaran

Department of Computer Engineering, Bahçeşehir University, Istanbul, Türkiye

Evolutionary Game Theory Image Inverse Problems

Jun 27, 2026cs.CV

Stochastic Optimal Control Sampling for Diffusion Inverse Problems

Benefiting from the strong ability to capture data distributions, diffusion models have become powerful tools for solving image inverse problems. The key is to controllably steer the sampling trajectory toward the measurements while respecting the diffusion prior. In this work, we introduce Stochastic Optimal Control Sampling (SOCS), which models the denoising process as a dynamical system and injects control signals via SOC. Previous SOC-based approach addresses inverse problems by optimizing over the entire trajectory, which is computationally expensive. In contrast, we derive a closed-form control update and apply it at each sampling step, pulling the measurement-consistent clean prediction back onto the denoising flow. In SOCS, we can readily modulate the control strength to align with the diffusion model's native capabilities and thereby enhance perceptual quality. Our method is compatible with a variety of linear stochastic differential equation backbones. Extensive experiments across a broad spectrum of image inverse tasks demonstrate that SOCS achieves accurate measurement-aligned reconstructions with improved visual fidelity and stronger quantitative performance.

Jie Zhang, Youmei Qiu, Hanling Tian +3

School of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China · Shanghai Key Laboratory of Flexible Medical Robotics, Tongren Hospital, Institute of Medical Robotics, Shanghai Jiao Tong University, Shanghai, China

Stochastic Optimal Control Diffusion-Based Inverse Problems Diffusion Posterior Sampling Image Inverse Problems