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

Jun 25, 2026eess.IV

Dual-Prior Guided Null-Space Learning with Mixture-of-Splines for Arbitrary Medical Slice Super-Resolution

Arbitrary slice super-resolution reconstructs isotropic volumes from anisotropic clinical acquisitions by synthesizing intermediate slices at arbitrary scales. However, treating this ill-posed inverse problem as unconstrained residual-based regression risks hallucinating anatomically implausible structures or altering the originally observed data. To address both concerns, this paper presents the Dual-Prior Null-space Learning (DP-NSL) framework, which reformulates the task as a constrained recovery process guided by two complementary priors. A Measurement-Consistent Projection (MCP) enforces a Deterministic Observation Prior: the reconstruction undergoes an exact orthogonal projection that reproduces every acquired slice with zero error, confining all learned details to the unobservable null space. Within this null space, a Mixture-of-Splines (MoS) module imposes a Geometric Continuity Prior by dynamically mixing B-spline experts of different analytic orders, allowing each anatomical region to be modeled with a content-aware level of continuity. To promote spatial coherence, a Local Spatial Consistency Decoder (LSCD) further injects local inductive bias. Experiments on three CT and one MRI benchmark show that DP-NSL outperforms existing approaches while strictly preserving measurement consistency. Code is available at https://github.com/DeepMed-Lab-ECNU/Medical-Image-Reconstruction.

Haofei Song, Siyuan Xu, Xintian Mao +3

Shanghai Key Laboratory of Multidimensional Information Processing, East China Normal University, Shanghai 200241, China

Image Reconstruction Medical Image Super-Resolution Inverse Problems Image Super-Resolution Image Inverse Problems

Jun 24, 2026cs.CV

Shift Variant Image Degradation and Restoration Using Singular Value Decomposition

Shift-variant image degradation is frequently encountered in practical imaging systems where the point spread function (PSF) varies across the image field due to motion, optical aberrations, atmospheric turbulence, or sensor-related effects. Unlike shift-invariant, shift-variant degradation presents significant challenges for image restoration because the degradation process cannot be represented by a single convolution kernel. This paper proposes a singular value decomposition (SVD)-based framework for restoring images degraded by shift-variant motion blur. The proposed approach determines the contribution of small singular values using a singular-value energy retention criterion. Specifically, the number of small singular values is selected based on a specified percentage of cumulative singular-value energy, providing a systematic approach for controlling noise amplification while preserving useful image information. The degradation model is formulated using a position-dependent PSF represented by a shift-variant imaging operator. Three representative one dimensional shift-variant motion PSFs are considered: bidirectional linear motion, Gaussian motion, and simple harmonic motion. The image degradation process is modeled as a linear system, and SVD is employed to analyze and invert the corresponding degradation operator. The singular-value representation provides insight into the ill-conditioned nature of the restoration problem and enables the development of stable inversion techniques. The proposed SVD-based restoration algorithm is applied to three degraded images. Experimental results demonstrate the effectiveness of the proposed approach in recovering image details and reducing blur artifacts under different motion models.

Arun D. Kulkarni

Computer Science Department at University of Texas at Tyler, Tyker, TX 75799 USA

Image Deblurring Image Restoration Image Inverse Problems

Jun 23, 2026cs.CV

What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View

A growing family of training-free solvers -- FlowDPS, FLOWER, PnP-Flow and their diffusion ancestors (DPS, DAPS) -- repurpose a pretrained flow-matching prior to solve imaging inverse problems by adding a measurement-guidance term to the deterministic probability-flow ODE. Despite strong empirical results, what these per-step corrections actually approximate -- and how far the resulting samples are from the true posterior

p(x\mid y)

-- has not been characterized. We give a posterior-transport account of flow-based inverse problem solving. Our starting point is a simple but consequential fact: for a \emph{deterministic} flow prior, Bayesian conditioning is realized entirely by a \emph{reweighting of the source distribution}, not by a drift correction; pushing the reweighted source through the \emph{unmodified} velocity field yields exact posterior samples. From this we show that trajectory-guidance solvers can be read as the minimum-kinetic-energy \emph{correction} field needed to morph the unconditional source into the posterior, and that FlowDPS / FLOWER / PnP-Flow correspond to distinct zeroth-order / Gaussian / proximal approximations of this single object; we bound the resulting posterior bias in Wasserstein distance. A controlled

2

D study with a closed-form posterior confirms the theory decisively: source reweighting matches the true posterior to the Monte-Carlo floor on every metric, whereas trajectory guidance incurs

200

--

800\times

larger error and collapses posterior modes, \emph{regardless of guidance strength}. Guided by the analysis we propose a cheap, principled velocity-correction solver that is competitive across two in-domain priors (AFHQ, CelebA) and two out-of-distribution settings while, unlike point-estimate source-space optimizers, producing diverse posterior samples with uncertainty that correlates with reconstruction error.

Jian Xu, Delu Zeng, John Paisley +1

1RIKEN iTHEMS · 2RIKEN AIP · 3South China University of Technology +1

Flow Matching Bayesian Inverse Problems Flow-Based Generative Modeling Image Inverse Problems

Jun 22, 2026physics.geo-ph

Tensor Train Decomposition-based 3D Implicit Full Waveform Inversion with Multi-scale Structural Similarity

Three-dimensional full waveform inversion (3DFWI) is a powerful technique for reconstructing high-resolution subsurface velocity models. However, its application is often limited by high memory requirements, computational costs, and sensitivity to cycle skipping. To overcome these challenges, we propose a novel tensor train (TT) decomposition-based 3D implicit full waveform inversion framework (TT-3DIFWI) combined with a multi-scale structural similarity (M-SSIM) objective function. In this framework, the 3D velocity model is represented by TT decomposition as a product of a series of low-rank core tensors. Then, three axis-specific implicit neural network representations (INR) based on one-dimensional vector coordinates as input are constructed to predict these core tensors, rather than directly predicting the velocity model. This INR reparameterization method based on TT decomposition can significantly reduce the memory consumption of INR training while maintaining the accuracy and resolution of the 3D velocity model reconstruction. Meanwhile, the low-rank structure of TT decomposition also ensures the structural consistency of the reconstruction velocity, thereby improving the accuracy and continuity of the inversion result. Furthermore, the M-SSIM objective function can compare the multi-scale structural differences between predicted and observed data, and utilize the ultra-low frequency features to reduce cycle skipping. Numerical experiments on synthetic and challenging land datasets demonstrate that TT-3DIFWI with M-SSIM achieves accurate and continuous velocity reconstruction, even with poor initial models or missing low-frequency data.

Liangsheng He, Chao Song, Tiansheng Chen +2

State Key Laboratory of Deep Earth Exploration and Imaging College of GeoExploration Science and Technology, Jilin University Changchun, Jilin, 130021, China · State Key Laboratory of DeepChaoEarthSong Exploration and Imaging College of GeoExploration Science and Technology, Jilin University Changchun, Jilin, 130021, China · Petroleum Exploration and Production Research Institute, Sinopec Beijing, 100083, China

Implicit Neural Representations 3D Reconstruction TT Decomposition Inverse Problems Image Inverse Problems

Jun 19, 2026eess.IV

Deep Unrolled Networks in Representation Space Applied to MRI Reconstruction

Deep unrolled networks (DUNs) integrate physical forward models with learned regularization in cascaded network architectures, achieving exceptional performance in inverse problems while maintaining interpretability. While most DUNs operate in the object domain (e.g., image space), recent variants explored representation spaces for improved information flow. However, these methods rely on heuristic methods for data consistency (DC), sacrificing fidelity with measurements. In this work, we introduce DUNE (Deep Unrolled Networks in rEpresentation space), a framework that maintains exact adherence to physical measurements while operating in learned representation spaces. By deriving the DC gradient via the chain rule and implementing it through the Vector-Jacobian Product (VJP), we enable exact backpropagation of measurement residuals into the representation space. This formulation supports diverse architectural backbones, including pre-trained encoders to guide the iterative process. We assess DUNE against state-of-the-art baselines on accelerated MRI reconstruction tasks, demonstrating that exact VJP-based gradients yield superior reconstruction quality and structural fidelity across both single-channel portable low-field and multi-channel clinical high-field MRI acquisitions. The code will be available upon publication at https://github.com/EfeIlicak/DUNE.

Efe Ilıcak, Baris Imre, Chloé Najac +4

Department of Radiology, Leiden University Medical Center, Leiden, Netherlands

Accelerated MRI Reconstruction Image Inverse Problems

Jun 19, 2026cs.CV

ShuffleFlow: Scalable Posterior Inference for Bayesian Inverse Imaging

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.

Tianao Li, Tjitske Starkenburg, Yu Sun +1

Department of Computer Science, Northwestern University, Evanston, IL 60208

Bayesian Inverse Problems Image Reconstruction Variational Inference Image Inverse Problems

Jun 18, 2026cs.LG

Flow Map Denoisers: Traversing the Distortion-Perception Plane for Inverse Problems

Image restoration faces a fundamental tradeoff: methods that minimize error produce blurry reconstructions, while those that maximize perceptual quality yield sharp but less faithful images. Existing approaches either commit to a single operating point on this distortion perception (DP) frontier or require paired-data supervision, auxiliary models, or hyperparameter tuning of the sampler to access different points. We show that flow map models, a recent extension of flow matching for few-step sampling that learns an average field, implicitly define a one-parameter family of denoisers that continuously spans the DP frontier. The lookahead parameter t acts as a control knob between the MMSE and perceptual regimes. For Gaussian targets, we prove that varying t exactly recovers the optimal DP frontier; for natural images, we observe similar behavior empirically. Within a Plug-and-Play solver, the same mechanism extends to general inverse problems, where it controls a tradeoff between perceptual alignment and data consistency. Despite the lack of exact optimality guarantees in this setting, a single trained flow map spans the DP tradeoff, matching or exceeding specialized baselines at both extremes. Extensive experiments on CelebA (

128\times 128

) and AFHQ (

256\times 256

) across several linear and nonlinear inverse tasks validate our findings.

Nicolas Zilberstein, Morteza Mardani, Santiago Segarra

Rice University · NVIDIA Inc.

Flow Matching Flow Map Learning Image Restoration Distortion-Perception Tradeoff Image Inverse Problems

Jun 16, 2026cs.LG

Blind Recovery of Latent Domains via Unsupervised Symmetry Discovery

Primary motivation in blind inverse problems is to recover signals of interest from corrupted observations without knowing the obfuscating mechanism. Blind deconvolution is a prominent approach when the corruption is convolutional, but it is not applicable when general linear transformations obfuscate the domain structure. In this work, we propose an unsupervised framework for recovering latent domains and signals by discovering symmetries of the data distribution. Our framework models observations as linear measurements of signals sampled from a latent random field, and optimizes a shallow group-convolutional network by imposing stationarity and locality regularization at the model output. The model learns a latent symmetry action and an appropriate filter, thereby mapping unstructured observations to a symmetry-based representation that reveals latent signals. Experiments on stochastic processes, Ising models, shuffled and bit-scrambled images, and neural recordings show that the method recovers latent domains and signals from unstructured observations, suggesting symmetry discovery as a new direction for unsupervised structure learning and blind inverse problems.

Onur Efe, Arkadas Ozakin

Physics Department, Bogazici University

Inverse Problems Image Inverse Problems

Jun 15, 2026cs.CV

LUCID: Learned Undersampling-Adaptive Consistency-Guided Inference with Deterministic Flow Matching for Sparse-View CT Reconstruction

Sparse-view CT reduces radiation dose and scanning time by acquiring fewer projection views, but angular undersampling makes reconstruction severely ill-posed, causing streak artifacts, structural blurring, and loss of fine details. Existing supervised methods are often tied to specific sampling settings, whereas generative methods may introduce anatomically inconsistent hallucination-like structures under severe undersampling. We propose Lucid, a sparsity-adaptive, consistency-guided reconstruction framework based on a Flow Matching generative prior for sparse-view CT. Lucid is trained only on high-quality CT images to learn a continuous transport between a Gaussian distribution and the high-quality CT image distribution, independent of view sampling. During inference, the sampling sparsity level is explicitly incorporated to adapt the generative trajectory of a single pretrained model. Specifically, Lucid constructs a degradation-matched initial state by sparsity-weighted fusion of the sparse-view FBP image and Gaussian noise, performs sparsity-modulated Flow Matching updates, and applies projection-domain data-consistency correction after each prior update. Experiments under multiple sparse-view settings show that Lucid achieves stable reconstruction performance across different sampling densities, improves image quality and structural fidelity, and reduces the risk of hallucination-like structures in generative sparse-view CT reconstruction.

Jigang Duan, Jiayi Wang, Heran Wang +3

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China · National Center for Applied Mathematics Beijing, Capital Normal University and Academy for multidisciplinary studies, Capital Normal University, Beijing, 100048, China

Sparse-View CT Reconstruction Computational Imaging Computed Tomography Image Inverse Problems

Jun 2, 2026cs.CV

Beyond Single Solution: Multi-Hypothesis Collaborative Deep Unfolding Network for Image Compressive Sensing

Recent deep unfolding networks (DUNs) have advanced Compressive Sensing (CS) by effectively integrating iterative optimization with deep learning architectures. However, most CS approaches predominantly confine their inference to a single solution space, neglecting the inherent ill-posedness of CS problems that intrinsically permits multiple plausible candidate hypotheses. In this paper, a novel Multi-Hypothesis Collaborative Deep Unfolding CS Network (MHC-DUN) is proposed, which explicitly models and leverages multiple hypotheses by jointly optimizing across diverse solution spaces. Specifically, following the Proximal Gradient Descent algorithm, MHC-DUN jointly performs gradient descent and proximal mapping within this multi-hypothesis paradigm. i) For gradient descent, a well-designed AlphaNet is introduced to dynamically predict spatially varying step sizes for all hypotheses, enabling collaborative gradient updates across multiple solutions. ii) For proximal operator, a sophisticated multi-hypothesis collaborative proximal mapping module is designed, which leverages both intra-hypothesis and inter-hypothesis correlation priors to jointly refine multiple solutions. To enable end-to-end training, a novel composite loss function is designed, which balances measurement fidelity, hypothesis diversity, and reconstruction accuracy, encouraging exploration of complementary solutions while maintaining reconstruction fidelity. Experimental results reveal that the proposed CS method outperforms existing CS networks.

Wenxue Cui, Hualin Li, Yuhang Qin +3

Harbin Institute of Technology, Harbin, China · Harbin Institute of Technology Suzhou Research Institute, Suzhou, China

Image Reconstruction Compressed Sensing Image Inverse Problems

Jun 1, 2026cs.CV

Hallucination-Aware Diffusion Sampling for Inverse Problems via Robust Prior Updates

Diffusion-based inverse problem solvers can produce realistic reconstructions, but realism alone does not ensure that the recovered details are supported by the measurement. We study this failure as measurement-conditioned hallucination: visually meaningful content that is either implausible or inconsistent with the measured instance. Our analysis separates Bayes-rule-based diffusion inverse solvers into a prior update and a measurement-conditioning step, showing that hallucinated content can enter through the prior-side proposal before the measurement correction is applied. Motivated by this view, we propose Robust Prior Update (RPU), a solver-level module that probes the local stability of the diffusion prior update, re-anchors the resulting displacement at the current iterate, and leaves the measurement update unchanged. We instantiate RPU in DPS and evaluate it on FFHQ and ImageNet inverse problems using automatic metrics and human faithfulness studies. On FFHQ, RPU improves PSNR and LPIPS over DPS across box inpainting, Gaussian deblurring, and motion deblurring. In human judgments, RPU receives 91.9% of blind non-tie majority preferences and 91.1% of ground-truth-assisted non-tie preferences on FFHQ box inpainting, while the ImageNet Gaussian reader study is tie-heavy but favors RPU among non-tie cases. These results support a targeted claim: robustifying the prior update can improve instance faithfulness in diffusion inverse solvers, especially when the prior shapes weakly constrained content.

Pengfei Jin, Yiqi Tian, Kailong Fan +2

Center for Advanced Medical Computing and Analysis, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114 · Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA 15261

Diffusion-Based Inverse Problems Hallucination Mitigation Diffusion Posterior Sampling Image Inverse Problems

Jun 1, 2026eess.SP

Physics-Aware Linearized ADMM and Its Unrolling

Recently, partial differential equations (PDEs) have been used to directly model the measurement process in signal processing, although their evaluation is costly. In this paper, we propose a novel alternating direction method of multipliers (ADMM)-based algorithm called physics-aware linearized ADMM (PA-LADMM) for inverse problems from PDE-based measurement processes. The key idea is the linearization of the subproblem with PDEs, leading to a cost-efficient update rule that calls only a PDE solver and its gradient evaluation per iteration. The algorithm has a theoretical convergence guarantee under certain conditions. In addition, we combine it with deep unfolding to unroll the PA-LADMM and train its internal parameters using supervised data. Two distinct experiments, compressed sensing with optical fiber communication and image restoration from noisy anisotropic diffusion, demonstrated the effectiveness of the proposed algorithms.

Satoshi Takabe, Shunta Arai, Tadashi Wadayama

Department of Computer Science Institute of Science Tokyo Tokyo, Japan · Center for Advanced Intelligence Project RIKEN Tokyo, Japan · Department of Engineering Nagoya Institute of Technology Nagoya, Japan

Alternating Direction Method of Multipliers Algorithm Unrolling Compressed Sensing PDE Inverse Problems Image Inverse Problems

May 28, 2026cs.LG

SubsurfaceGen: Procedural Generation of Field-Scale Earth Models and Seismic Data

Full waveform inversion (FWI) is the gold standard for subsurface imaging, with applications from carbon sequestration to energy and mineral exploration to earthquake hazard assessment. Machine learning approaches to FWI need field-scale, geologically diverse, and physically realistic training data, but existing resources such as Marmousi, SEAM, and OpenFWI fall short on spatial extent, temporal extent, geological diversity, and physical realism. We address these limitations with SubsurfaceGen, a GPU-accelerated generator for 3D velocity models and seismic data. Along with SubsurfaceGen, we release a paired dataset of 4,276 2D velocity slices, 5 s wavefields, and 8 s shot gathers drawn from 42 realistic, field-scale 3D velocity models, each spanning 10 km x 10 km laterally and 6.19 km deep at 10 m resolution. The dataset spans six geological settings -- four built with SubsurfaceGen and two drawn from prior sources -- relevant for carbon sequestration and hydrocarbon exploration. We use this dataset to evaluate neural operators on wavefield prediction and encoder-decoders on end-to-end velocity inversion, holding out one geological setting for out-of-distribution testing. These experiments surface failure modes at field-scale and demonstrate how SubsurfaceGen and the associated dataset can impact ML-based FWI.

Joseph Stitt, Pratik Rathore, Madeleine Udell +1

Stanford University

Synthetic Data Generation PDE Surrogate Modeling Synthetic Benchmark Generation Seismology Inverse Problems Image Inverse Problems

May 27, 2026cs.CV

Trajectory Constraints for Imaging Inverse Problems

Diffusion-based and iterative methods have become effective tools for solving imaging inverse problems. Their reconstruction process naturally forms a trajectory of intermediate estimates. Although these intermediate estimates define a reconstruction trajectory, most methods do not explicitly regularize the transitions between consecutive states. To address this limitation, we introduce TRACE, a training-free TRAjectory-Constrained rEconstruction framework that stabilizes the reconstruction path by coupling adjacent states along the trajectory. This gives a trajectory-level model that can be interpreted as a sequence of proximal updates. Since the exact proximal update is generally intractable, we approximate it with a neural mapping. This yields a diffusion-like reconstruction process with an explicit coupling between neighboring states. We provide a stability analysis showing that temporal coupling bounds trajectory variation and that this control is preserved under untrained network updates. Experiments on linear and nonlinear image reconstruction tasks show that TRACE improves reconstruction quality. Trajectory-level analyses and ablations confirm that temporal coupling directly affects state transitions along the reconstruction path.

Chaoyan Huang, Haijie Yuan, Saiprasad Ravishankar

Department of Computational Mathematics, Science, & Engineering, Michigan State University · Department of Electrical Engineering and Computer Science, University of Michigan · Department of Biomedical Engineering, Michigan State University

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

May 27, 2026cs.CV

Bound-Constrained Sparse Representation for Electrical Impedance Tomography

This study proposes a bound-constrained sparse representation (BC-SR) framework for electrical impedance tomography (EIT), aimed at improving conductivity estimation without explicit regularization. BC-SR adopts a representation-driven strategy, generating conductivity from low-dimensional latent variables via an implicit composite parameterization. Structural priors are embedded using a truncated graph-Laplacian basis, while a bound-preserving nonlinear mapping enforces admissible conductivity ranges and improves conditioning through implicit gradient modulation. The approach ensures robust convergence, even under noisy or incomplete data. Extensive validation on 2D/3D simulations, tank experiments, and in-vivo lung data shows that BC-SR improves physical consistency and structural fidelity, offering enhanced robustness compared to traditional methods. Additionally, BC-SR enables 3D time-difference EIT reconstruction, offering improved spatial resolution and a more coherent representation of 3D conductivity distributions, particularly for in-vivo lung data. This suggests potential for improved performance in EIT, particularly in clinical applications for respiratory monitoring.

Chun Zhang, Dong Liu

School of Biomedical Engineering and Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China · Laboratory of Spin Magnetic Resonance and Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China · Jiangsu Provincial Key Laboratory of Multimodal Digital Twin Technology, Suzhou 215123, China

Sparse Recovery Image Reconstruction Constrained Optimization Image Inverse Problems

May 26, 2026eess.IV

Unsupervised Deep Image Prior for Sparse-View and Limited-Angle Electron Tomography

Electron tomography (ET) plays an important role in the three-dimensional (3D) characterization of nanomaterials. However, under limited-angle and sparse-view conditions, conventional algorithms produce degraded reconstructions, which compromise the quality and interpretability of resulting 3D data. In this paper, we present deep image prior (DIP), an unsupervised deep learning (DL) approach, for highly degraded tomography acquisitions and demonstrate, using simulated data, that its performance is comparable to that of supervised approaches requiring training datasets, even for tilt ranges as limited as 60° and tilt increments of 10°. We then apply it to experimental data and show that it enables reliable 3D quantification under both sparse-view and limited-angle conditions, highlighting its potential for a wide range of materials and acquisition modalities.

Serge Brosset, Daniel del Pozo Bueno, Thomas David +3

a Univ. Grenoble Alpes, CEA, Leti, F-38000 Grenoble, France. · b Univ. Grenoble Alpes, CEA, Liten, F-38000 Grenoble, France. · c CEA, Joliot, NeuroSpin, Gif-sur-Yvette Cedex 91191, France. +1

Sparse-View CT Reconstruction Computed Tomography Image Inverse Problems

May 26, 2026cs.CV

A Viscosity Semigroup Framework for Stable Image Reconstruction

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.

Arina Oberoi

Image Reconstruction Image Inverse Problems

May 26, 2026cs.CV

Triadic Dynamics Aware Diffusion Posterior Sampling for Inverse Problems: Optimizing Guidance and Stochasticity Schedules

Generative posterior sampling using diffusion models has emerged as a dominant paradigm for solving inverse problems in imaging, which usually consists of three main components: data consistency (DC) guidance, classifier-free guidance (CFG) and stochasticity. While prior arts have focused on how to develop each or all components, less attention has given to how to schedule them, leading to heuristically fixed or partially adjusted suboptimal schedules. In this work, we argue that the interactions among all three components in terms of scheduling are crucial for significantly improved performance in solving inverse problems in imaging. Our analysis shows that aggressive CFG early in sampling conflict with DC guidance, while stochasticity brings the trajectory back to higher-probability regions. Based on these findings, we propose Triadic Dynamics Aware Posterior Sampling (TriPS), which reformulates posterior sampling as a time-varying control problem and optimizes schedules following a triadic trend of decreasing DC and stochasticity scales alongside increasing CFG scale. TriPS achieves this through two strategies: template-based search over functional priors for reliable baseline schedules, and Group Relative Policy Optimization (GRPO)-based reinforcement learning for more flexible temporal curves. Experiments demonstrate TriPS outperforms state-of-the-art baselines in data fidelity and perceptual realism.

Junseo Bang, Dong Ju Mun, Hoigi Seo +2

Dept. of Electrical and Computer Engineering · INMC · IPAI & AIIS

Diffusion Model Guidance Diffusion Timestep Scheduling Diffusion-Based Inverse Problems Diffusion Posterior Sampling Image Inverse Problems

May 24, 2026cs.CV

A Principled Self-Referenced Early Stopping Approach for Deep Image Prior

Recently, Deep Image Prior (DIP) has demonstrated strong capabilities for solving inverse imaging problems (IIPs) by optimizing a randomly initialized convolutional neural network in a training-data-free regime. However, DIP suffers from overfitting to noisy measurements due to network over-parameterization, making early stopping (ES) essential. The most successful ES method tracks fluctuations in the running variance of the network output to detect overfitting. However, in many applications, these fluctuations may appear prematurely, leading to unstable reconstructions. In this paper, we first show that nearly optimal DIP early stopping can be achieved when two independent noisy copies of the degraded image are available. Motivated by this observation, and since obtaining two fully independent copies is infeasible, we propose an overfitting detection framework based on constructing pseudo self-referenced images, resulting in three IIP-specific algorithms. Our approach is further supported by theoretical results on single-reference validation, pseudo-validation estimation, and the impact of shared noise. Across different IIPs, ranging from natural image restoration to medical image reconstruction, and under varying noise levels and noise types, our methods consistently outperform existing DIP early stopping approaches, all without requiring an accurate estimate of the noise level.

Chaoyan Huang, Cheng-Han Huang, Ismail R. Alkhouri +1

Department of Computational Mathematics, Science, & Engineering, Michigan State University · Department of Electrical Engineering and Computer Science, University of Michigan · X Computational Physics Division, Los Alamos National Laboratory +2

Early Stopping Image Reconstruction Image Restoration Image Inverse Problems

May 22, 2026cs.CV

Single View Seafloor Recovery from Imaging Sonar via Differentiable Rendering

Sonar is often the only modality suitable for high-resolution imaging underwater due to light attenuation and turbidity. Forward-looking imaging sonar provides measurements over range and horizontal angle but collapses vertical structure into a flat image, creating ambiguities that make 3D recovery challenging. A common use case for imaging sonar is underwater terrain mapping (bathymetry), yet current methods require many views, expensive multi-sensor setups, or significant training data, which limits use and adaptability to new environments. We present a training-free method that recovers bathymetry from a single sonar image in under 30 seconds via differentiable rendering, conditioned on a known seafloor tilt. To our knowledge, this is the first differentiable rendering approach for single-view height recovery in sonar. Our method implements differentiable sonar ray tracing and optimizes an explicit height field to reproduce the target image. On synthetic datasets, our approach outperforms a supervised CNN under distribution shift and remains close on rough terrain, while the CNN wins in-distribution. By modeling physically grounded priors of the sonar process, our method adapts across sensor configurations and environments without training data.

Sevan Brodjian, Michael Hobley, Pietro Perona

California Institute of Technology

Differentiable Rendering Underwater Imaging Depth Estimation Underwater 3D Reconstruction Single-View 3D Reconstruction Image Inverse Problems

May 20, 2026cs.LG

UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problems

We investigate unpaired image inverse problems, a challenging setting where only independent, non-paired sets of noisy measurements and clean target signals are available for training. We propose a novel inverse problem solver based on Unbalanced Optimal Transport, called Unbalanced Optimal Transport Map for Inverse Problems (UOTIP). Our method formulates the reconstruction task, predicting clean target signals from noisy measurements, as learning a UOT Map from noisy measurement distribution to clean signal distribution by incorporating a likelihood-based cost function. By relaxing the exact marginal constraint, the UOT framework provides key advantages to our model: robustness to multi-level observation noise, adaptability to class imbalance between noisy and clean datasets, and generalizability to diverse noise-type scenarios. Furthermore, we theoretically demonstrate that incorporating a quadratic cost term ensures the existence and uniqueness of the transport map by satisfying the twist condition, even for ill-posed inverse problems. Our experiments demonstrate that UOTIP achieves state-of-the-art performance on unpaired image inverse problem benchmarks, across linear and nonlinear inverse problems.

Donggyu Lee, Taekyung Lee, Jaewoong Choi

Department of Mathematical Sciences, Seoul National University · IPAI (Interdisciplinary Program in Artificial Intelligence, Seoul National University) · Sungkyunkwan University

Image Reconstruction Optimal Transport Image Inverse Problems

May 15, 2026cs.LG

Learning Normalized Energy Models for Linear Inverse Problems

Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations:

(i)

the prior density is represented implicitly, and

(ii)

they rely on likelihood approximations that introduce sampling biases. We address these challenges by introducing a new energy-based model trained for denoising with a covariance-based regularization term that enforces consistency across different measurement conditions. The trained model can compute normalized posterior densities for diverse linear inverse problems, without additional retraining or fine tuning. In addition to preserving the sampling capabilities of diffusion models, this enables previously unavailable capabilities: energy-guided adaptive sampling that adjusts schedules on-the-fly, unbiased Metropolis-Hastings correction steps, and blind estimation of the degradation operator via Bayes rule. We validate the method on multiple datasets (ImageNet, CelebA, AFHQ) and tasks (inpainting, deblurring), demonstrating competitive or superior performance to established baselines.

Nicolas Zilberstein, Santiago Segarra, Eero Simoncelli +1

Rice University, Houston, TX, USA · Flatiron Institute, New York, NY, USA · New York University, New York, NY, USA

Bayesian Inverse Problems Energy-Based Models Diffusion-Based Inverse Problems Diffusion Posterior Sampling Inverse Problems Image Inverse Problems

May 14, 2026eess.IV

DIPA: Distilled Preconditioned Algorithms for Solving Imaging Inverse Problems

Solving imaging inverse problems has usually been addressed by designing proper prior models of the underlying signal. However, minimizing the data fidelity term poses significant challenges due to the ill-conditioned sensing matrix caused by physical constraints in the acquisition system. Thus, preconditioning techniques have been adopted in classical optimization theory to address ill-conditioned data-fidelity minimization by transforming the algorithm gradient step to achieve faster convergence and better numerical stability. We extend the preconditioning concept beyond convergence acceleration and use it to improve reconstruction quality. We introduce DIPA: Distilled Preconditioned Algorithms, where a preconditioning operator (PO) is optimized using teacher-guided distillation criteria. Unlike standard model-compression KD, the teacher and student differ by the sensing operators available during reconstruction: the teacher uses a simulated, better-conditioned, and more informative sensing matrix, whereas the student uses the physically feasible sensing matrix. We design different distillation loss functions to transfer different properties of the teacher algorithm to the preconditioned student. The PO can be linear (L-DIPA), allowing interpretability, or non-linear (N-DIPA), parametrized by a neural network, offering better scalability. We validate the proposed PO design across several imaging modalities, including magnetic resonance imaging, compressed sensing, and super-resolution imaging.

Romario Gualdrón-Hurtado, Roman Jacome, Leon Suarez +1

Department of Computer Science, Universidad Industrial de Santander, Bucaramanga, 680002, Colombia · Department of Electrical Engineering, Universidad Industrial de Santander, Bucaramanga, 680002, Colombia

Learning to Optimize Image Reconstruction Knowledge Distillation Image Inverse Problems

May 14, 2026physics.geo-ph

Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel

Full-waveform inversion (FWI) estimates unknown parameters in the wave equation from limited boundary measurements. Recent advances in neural reparameterized FWI (NeurFWI) demonstrate that representing the parameters using a neural network can reduce the reliance on the high-quality initial model and wavefield data, at the cost of slow high-resolution convergence. However, its underlying theoretical mechanism remains unclear. In this study, we establish the neural sensitivity kernel (NSK) and the wave tangent kernel (WTK) to analyze their convergence behavior from both model and data domains. These theoretical frameworks show that the neural tangent kernel (NTK) induced by neural representation adaptively modulates the original sensitivity and wave tangent kernels. This modulation leads to several key outcomes, i.e., the spectral filtering effect, the gradient wavenumber modulation, and the wave frequency bias, connecting the convergence behavior of NeurFWI with the eigen-structures of NSK and WTK. Building on these insights, we propose several enhanced NeurFWI methods with tailored eigen-structures in NSK and WTK to improve inversion performances and efficiency. We numerically validate these theoretical claims and the proposed methods in seismic exploration, and firstly extend their application to medical imaging.

Ruihua Chen, Yisi Luo, Bangyu Wu +2

School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China · School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, China · School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610000, China

Neural Tangent Kernel Inverse Problems Image Inverse Problems

May 13, 2026cs.CV

Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration

Image restoration is an inherently ill posed inverse problem. Equivariant networks that embed geometric symmetry priors can mitigate this ill posedness and improve performance. However, current understanding of the relationship between network equivariance and data symmetry remains largely heuristic. Particularly for real world data with imperfect symmetry, existing research lacks a systematic theoretical framework to quantify symmetry, select transformation groups, or evaluate model data alignment. To bridge this gap, we conduct an analysis from an optimization perspective and formalize the intrinsic relationship among data symmetry priors, model equivariance, and generalization capability. Specifically, we propose for the first time a quantifiable definition of non strict symmetry at the dataset level (rather than sample level) and use it as a constraint to formulate the restoration inverse problem. We then show that the equivariance for restoration models can be naturally derived from this inverse problems incorporated the proposed symmetry constraints, and that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size. Furthermore, by analyzing the network's empirical risk, we demonstrate that aligning equivariance with data symmetry optimizes the bias variance trade off, minimizing the total expected risk. Guided by these insights, we propose a Sample Adaptive Equivariant Network that uses a hypernetwork and transformation learnable equivariant convolutions to dynamically align with each sample's inherent symmetry. Extensive experiments on super resolution, denoising, and deraining validate our theoretical findings and show significant superiority over standard baselines and traditional equivariant models. Our code and supplementary material are available at https://github.com/tanfy929/SA-Conv.

Feiyu Tan, Qi Xie, Zongben Xu +1

School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi, China

Equivariant Neural Networks Image Restoration Image Inverse Problems Image Denoising

May 13, 2026physics.optics

DeepFilters: Scattering-Aware Pupil Engineering with Learned Digital Filter Reconstruction for Extended Depth of Field Microscopy

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.

Joseph L. Greene, Suet YIng Chan, Qilin Deng +8

Boston University, Department of Electrical and Computer Engineering, Boston, MA, 02215 · Current Address: Georgia Tech Research Institute, Electro-Optical Systems Lab, Atlanta, GA, 30332 · Boston University, Department of Biology, Boston, MA, 02215 +3

Image Reconstruction Microscopy Image Analysis Image Inverse Problems

May 13, 2026cs.CV

Bayesian In Vivo Tracking of Synapses using Joint Poisson Deconvolution and Diffeomorphic Registration

Synapses are densely packed submicron structures that dynamically reorganize during learning and memory formation. Longitudinal \textit{in vivo} imaging of fluorescently tagged synaptic receptors offers a promising opportunity to study large-scale synaptic dynamics and how these processes are disrupted in neurological disease. However, in vivo imaging with 2-photon microscopy uses low laser power and therefore suffers from low signal-to-noise ratio (SNR) and high shot noise, nonlinear tissue motion between days, nonstationary fluctuations in synaptic fluorescence, and significant blur induced by the microscope point spread function (PSF). Together, these factors make it challenging to detect and track synapses, especially in regions with high synaptic density. This paper presents a novel template-based framework for modeling synapses as varying luminance point sources that move under a nonlinear tissue deformation. Taking a unified Bayesian approach, we apply this model to microscopy data by deriving a posterior that incorporates a diffeomorphic mapping for domain warping, a Gaussian point spread function for the imaging process, and a Poisson observation model for raw photon counts. The Bayesian solution simultaneously: (1) Constructs a probabilistic template of synapse locations, (2) denoises and deconvolves the image data, (3) infers fluorescence intensities, (4) performs diffeomorphic image registration to correct for tissue motion, and (5) provides confidence regions for these parameter estimates. We demonstrate the framework on both a 2D+t simulated dataset and a 3D+t longitudinal \textit{in vivo} microscopy dataset of fluorescent synapses imaged in a mouse over two weeks.

Shashwat Kumar, Dominic M. Padova, Binish Narang +6

Department of Biomedical Engineering, Johns Hopkins University · Department of Neuroscience, Johns Hopkins University · Kavli Neuroscience Discovery Institute, Johns Hopkins University +2

Bayesian Inverse Problems Longitudinal Medical Image Analysis Neuroimaging Microscopy Image Analysis Image Inverse Problems

May 12, 2026cs.CV

Beyond MMSE: Enhancing PnP Restoration with ProxiMAP

Plug-and-Play (PnP) methods have become standard tools for solving imaging inverse problems by replacing the intractable maximum a posteriori (MAP) denoiser with the MMSE one. While this mismatch has been widely treated as unavoidable, recent works have sought to close this gap by targeting the MAP with diffusion-model scores. We show this is problematic in practice: learned scores do not match the true ones, so MAP-targeting iterations converge to cartoon-like images rather than realistic ones, and better results are obtained by stopping short of convergence. We turn this observation into a design principle and introduce ProxiMAP, an iterative MAP approximation whose noise schedule keeps the iterate's residual noise matched to the denoiser's training noise. This keeps the denoiser in-distribution where its score is reliable, and yields implicit early stopping that avoids the failure mode above. ProxiMAP is a modular drop-in replacement for MMSE denoisers in standard PnP algorithms and consistently sharpens reconstructions across deblurring, inpainting, super-resolution, and phase retrieval. Building on the same principle, we propose a hybrid variant that applies ProxiMAP only in the late iterations of PnP, where the denoiser is most reliable -- matching or exceeding the full-replacement variant at a fraction of the cost.

Kenta Vert, Giacomo Meanti, Scott Pesme +2

1Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK · 2MaLGa Centre, DIBRIS, Università di Genova, MMS, Italian Institute of Technology, Genova, Italy

Diffusion Models for Image Restoration Computational Imaging Image Restoration Image Inverse Problems

May 12, 2026cs.CV

Improving Diffusion Posterior Samplers with Lagged Temporal Corrections for Image Restoration

Diffusion-based posterior sampling (PS) is a leading framework for imaging inverse problems, combining learned priors with measurement constraints. Yet, its standard formulations rely on instantaneous data-consistent estimates, which induce temporal variability in the reverse dynamics. We reinterpret PS from a dynamical perspective, showing that the standard PS update corresponds to a first-order discretization of the diffusion dynamics plus a residual correction capturing the mismatch between the denoised prediction and the data-consistent estimate. A second-order discretization, however, naturally introduces a temporal correction based on the variation of consecutive estimates. Building on this, we propose LAMP, combining the second-order update with the residual correction characterizing a PS technique. LAMP thus inherits a lagged temporal correction, and it can be implemented as a modular plug-in over the PS backbone. We show that LAMP preserves the structure of a posterior sampler, and we perform a one-step risk analysis to characterize when LAMP improves the reverse transition via a bias-variance trade-off. Experiments across multiple imaging tasks demonstrate consistent improvements over strong baselines such as DiffPIR and DDRM, without increasing the number of denoising evaluations.

Davide Evangelista, Elena Morotti, Francesco Pivi +1

Dept. of Computer Science and Engineering University of Bologna · Dept. of Political and Social Sciences University of Bologna

Diffusion Sampling Image Restoration Diffusion-Based Inverse Problems Diffusion Posterior Sampling Image Inverse Problems

May 12, 2026cs.CV

When Brains Disagree: Biological Ambiguity Underlies the Challenge of Amyloid PET Synthesis from Structural MRI

Structural MRI-to-amyloid PET synthesis has been proposed as a non-invasive alternative for amyloid assessment in Alzheimer's disease (AD). However, reported performance of identical models varies widely across studies, and increasingly complex architectures have not led to consistent gains. This inconsistency is thought to be caused by a fundamental biological ambiguity: MRI captures neurodegeneration, while PET measures amyloid pathology - two processes that are often temporally decoupled in AD. As a result, similar MRI patterns may correspond to different amyloid states, creating ambiguous one-to-many mappings. MRI-to-amyloid PET synthesis may therefore be intrinsically ill-posed; however, this idea has yet to be tested scientifically. The aim of this work is to test this hypothesis through two controlled experiments. We first control the training distribution by stratifying paired MRI-PET data by amyloid and neurodegeneration status. Using two standard synthesis models under a controlled design, we show that biologically unambiguous mappings are learnable in isolation, but performance collapses when data ambiguity is introduced. This demonstrates that ambiguity in the data distribution, rather than architectural capacity, constrains performance. Second, we show that introducing orthogonal biological information in the form of plasma biomarkers resolves this ambiguity. When multimodal inputs are incorporated, performance improves and stability is restored. Together, these findings suggest that limited and inconsistent performance in MRI-to-amyloid PET synthesis is explained by intrinsic biological ambiguity, and that stable, meaningful progress requires multimodal integration rather than architectural complexity.

Louise E. G. Baron, Ross Callaghan, David M. Cash +3

Hawkes Institute, University College London, UK · Department of Medical Physics and Biomedical Engineering, University College London, UK · AINOSTICS Ltd, Manchester, UK +3

Alzheimer's Disease Medical Image Synthesis Image Inverse Problems