Special Session 32: Inverse Problems and Image Processing

AFIRE: Accurate and Fast Image Reconstruction Algorithm for Geometric-Inconsistent Multispectral CT

Chong Chen Chinese Academy of Sciences Peoples Rep of China Co-Author(s):    Yu Gao

Abstract: Multispectral computed tomography (MSCT) has attracted increasing attention and research interest due to the development of hardware and requirement of applications, as well as its advantages in considering the X-ray energy-dependent information over the conventional CT such as artifact suppression, contrast improvement and object separation. However, accurate and fast image reconstruction in MSCT remains a challenging task, largely because its data model is nonlinear, and the scanning geometry parameters under different X-ray energy spectra are sometimes inconsistent or mismatched. In this talk, we will discuss our recent advances on algorithm and theory for the image reconstruction in geometric-inconsistent MSCT.

An efficient augmented Lagrangian method for dynamic optimal transport based on second-order cone programming

Liang Chen Hunan University Peoples Rep of China Co-Author(s):    Youyicun Lin, Yuxuan Zhou

Abstract: This talk introduces an efficient numerical approach to solve dynamic optimal transport (DOT) problems with quadratic cost in Euclidean spaces or on surfaces, computing both the quadratic Wasserstein distance and the associated displacement interpolation. Building on the convex DOT model of Benamou and Brenier, we reformulate the discretized dual DOT problem to a linear second-order cone programming (SOCP) problem. Then, by taking advantage of the SOCP reformulation, we can solve them efficiently by a computationally highly economical implementation of an inexact symmetric Gauss-Seidel decomposition-based proximal augmented Lagrangian method, which converges to a Karush-Kuhn-Tucker solution without any additional assumptions. Implemented as open-source software packages, the proposed approach demonstrates robustness, effectiveness, and superior computational efficiency in extensive numerical experiments on various datasets, achieving a several-fold speed-up over the state-of-the-art solvers. Additionally, it exhibits robustness to problems with densities that lack a positive lower bound.

Physics-Driven Deep Learning for CT Metal Artifact Reduction

Zhangling Chen Tianjin Normal University Peoples Rep of China Co-Author(s):

Abstract: This report will introduce two types of CT metal artifact reduction (MAR) methods based on the fusion of physical priors and deep learning. The first is a deep unrolling framework with soft metal trace, which adopts an adaptive projection-domain weighting mechanism to preserve effective tissue information and integrates a physics-informed primal dual hybrid gradient optimization scheme into the network to enhance model interpretability. The second is a self-supervised framework based on implicit neural representation, which does not require paired data, combines multi-resolution hash encoding to capture high-frequency anatomical information, and incorporates physical correction operators and an adaptive bone region weighting strategy to achieve simultaneous correction of metal and bone regions.

Segmenting Objects with Imbalanced Sizes via Smooth and Sparse Dual Optimal Transport

LI CUI School of Mathematical Science, Beijing Normal University Peoples Rep of China Co-Author(s):    Mengqi Ding, Gangxuan Zhou, Xue-Cheng Tai, Li Cui, Jun Liu

Abstract: To address imbalanced object sizes in image segmentation, this work formulates the problem via optimal transport theory and a Laguerre cell decomposition. The dual variable of the volume constraint is interpreted as a learnable bias, and an iterative network-embedding laye (VP-Sparsemax) is proposed to solve the smooth semi-dual formulation while incorporating spatial information. Compared to softmax, VP-Sparsemax improves volume preservation after argmax due to its sparsity. Experiments on four dataset across three segmentation baselines demonstrate superior performance, especially for small targets that are easily overlooked.

NCHG-Seg: Nerve-Prioritized Multi-Scale Tissue Segmentation and Nerve-Centric Heterogeneous Graph Learning for Perineural Invasion Modeling and Survival Prediction in Pancreatic Cancer

Luying Gui Nanjing University of Science and Technology Peoples Rep of China Co-Author(s):    Ma Rukang; Han Wennan; Wang Bingxue

Abstract: Perineural invasion (PNI) is a pivotal prognostic indicator in pancreatic cancer, yet accurate quantification is hindered by subjective assessment and imprecise tissue segmentation. We propose NCHG-Seg, an integrated framework that introduces a nerve-prioritized multi-scale segmentation module and a nerve-centric heterogeneous graph (NCHG) for precise tumor--nerve interaction modeling. The segmentation augments a Swin Transformer with nerve-prior attention and boundary-aware refinement, yielding high-fidelity nerve, tumor, and microenvironment masks from gigapixel WSIs. These masks enable hierarchical graph construction with intra-tumoral nodes defined by geometric containment and boundary proximity, followed by a biologically inspired dual-attention message-passing mechanism (Structural Attention and Feature Similarity Attention). Experiments across three multicenter cohorts (TCGA-PAAD, GULOU, SZY) show that NCHG-Seg achieves a C-index of 0.6437 and AUC of 0.6857 on TCGA-PAAD, outperforming state-of-the-art WSI-based survival models with strong cross-center generalization. Our approach offers an interpretable tool for quantitative PNI assessment in precision oncology.

Mixed geometry information regularization for image deblurring with multiplicative noise

Zhichang Guo Harbin Institute of Technology Peoples Rep of China Co-Author(s):

Abstract: We propose a variational model for the simultaneous removal of multiplicative noise and blur. Variational regularization techniques have been widely employed in various image processing tasks. However, designing models that incorporate sufficient geometric priors remains a challenging problem. To address this issue, we introduce a mixed geometry regularization that integrates both area and curvature terms as priors. Due to the high-order and nonlinear nature of the model, minimizing the associated functional is nontrivial. To overcome this challenge, we adopt the additive operator splitting method and a relaxed scalar auxiliary variable (RSAV) approach, with the latter showing higher computational accuracy for our model. The unconditional stability of these algorithms allows the use of a large time step. Furthermore, we discuss several theoretical properties of the RSAV method. Numerical experiments demonstrate the effectiveness of the proposed model and the efficiency of the corresponding algorithm. Extensive results indicate that our model can effectively address both image deblurring and multiplicative noise removal simultaneously.

Variational Framework for Image Vectorization and Applications

Roy Yuchen He City University of Hong Kong Hong Kong Co-Author(s):

Abstract: Images are commonly represented as bitmaps, making it essential to identify the intrinsic geometric features of objects from such unstructured data. Vectorization is a widely used technique that converts raster images into collections of parametric curves and surfaces, capturing the input`s prominent features while yielding resolution-independent representations. In this talk, we propose variational principles for image vectorization, together with efficient algorithms based on the affine shortening flow and region merging, generalizing steepest gradient descent for the reduced Mumford-Shah functional. We also present recent applications in shape classification and historical glyph preservation.

Quadratic convergence of the Gauss-Newton method for complex phase retrieval

Meng Huang Beihang University Peoples Rep of China Co-Author(s):

Abstract: We introduce a Gauss-Newton method for solving the complex phase retrieval problem. In contrast to the real-valued setting, the Gauss-Newton matrix for complex-valued signals is rank-deficient and, thus, non-invertible. To address this, we utilize a Gauss-Newton step that moves orthogonally to certain trivial directions. We establish that this modified Gauss-Newton step has a closed-form solution, which corresponds precisely to the minimal-norm solution of the associated least squares problem. Additionally, using the leave-one-out technique, we demonstrate that $m\ge O( n\log^3 n)$ independent complex Gaussian random measurements ensures that the entire trajectory of the Gauss-Newton iterations remains confined within a specific region of incoherence and contraction with high probability. This finding allows us to establish the quadratic convergence rate of the Gauss-Newton method without the need of sample splitting.

A Gaussian Mixture-Based Sequential Monte Carlo Algorithm for Solving Infinite-Dimensional Statistical Inverse Problems

Junxiong Jia Xi`an Jiaotong University Peoples Rep of China Co-Author(s):    Haoyu Lu

Abstract: In this talk, we introduce a sequential Monte Carlo (SMC-GM) algorithm equipped with a Gaussian mixture transition kernel. This algorithm is designed to improve the efficiency of sampling from the posterior measure in infinite-dimensional Bayesian inverse problems. We establish the denseness of Gaussian mixture measures with respect to the total variation distance in separable Hilbert spaces, which serves as the foundation for our convergence theory. Additionally, we propose a well-defined preconditioned Crank-Nicolson method with a Gaussian mixture prior (pCN-GM) for use in infinite-dimensional function spaces. By leveraging the denseness of Gaussian mixture measures and the invariance of the pCN-GM transition kernel, we provide a convergence theorem for SMC-GM. In our numerical experiments, we apply this method to a nonlinear Darcy flow statistical inverse problem, confirming its high sampling efficiency, low error, capability to sample complex posteriors, and dimension-independence.

Image Inverse Problems with Generative Priors

Ji Li Capital Normal University Peoples Rep of China Co-Author(s):    Ji Li

Abstract: The design of image prior representations is pivotal to solving image inverse problems. With the recent rapid development of deep learning, image priors have evolved from traditional expert-designed and data-driven representations to those learned via generative models. More precise image priors undoubtedly lead to enhanced performance in computational imaging tasks. This talk first provides a brief introduction to the paradigm of learning data distributions using Ordinary Differential Equation (ODE)-controlled generative models. Subsequently, we discuss two perspectives on applying generative priors to image inverse problems: conditional sampling and plug-and-play fusion methods. Finally, the talk outlines the core concepts and computational frameworks of generative algorithms for image inverse problems.

Boosting Adversarial Transferability via Multi-anchor Probability Manifold Priors

Yao Li Harbin Institute of Technology Peoples Rep of China Co-Author(s):    Yao Li

Abstract: In real-world black-box attack scenarios, transferability is the primary threat vector. Targeted attacks, while of high practical importance, are notoriously difficult to transfer across models with heterogeneous architectures. This work introduces a Probability Manifold Framework that quantifies the intrinsic density of high-dimensional data by implicitly modeling the geometry of its underlying low-dimensional manifold. We theoretically prove that our density measure monotonically reflects the distance from a sample to the data manifold and demonstrate that guiding adversarial perturbations toward High-Sample-Density Regions (HSDR) is the optimal strategy for improving targeted transferability. To generalize this guidance to arbitrary feature topologies, we devise a topology-aware Multi-Anchor Softmin Strategy. This approach enables adaptive matching to valid high-density modes instead of forcing a rigid approximation to a single centroid, thereby avoiding low-density voids and accelerating convergence. Building on these innovations, we propose MAGMA (Multi-Anchor Generative Manifold Attack), a novel generative method for targeted attacks. Extensive experiments on ImageNet show that MAGMA sets a new state-of-the-art for generative attacks, substantially outperforming existing methods (e.g., TTP, ESMA) in average transfer success rate while also achieving significant gains in training efficiency.

Geometry-Aware Super-Resolution Imaging

Yutong Li Tianjin Normal University Peoples Rep of China Co-Author(s):

Abstract: Super-resolution fluorescence microscopy enables nanoscale visualization of subcellular structures, high-performance reconstruction algorithms are imperative for further improving imaging quality. To improve the spatial resolution of fluorescence microscopy images, we present a deconvolution algorithm GEOREC, which is a robust and efficient super-resolution reconstruction framework. A background term is incorporated to achieve dynamic and precise removal of background fluorescence. We further integrate the geometric prior derived from shape operator in the model to preserve the sharp edges of the structure during denoising and background removal. In addition, we adopt a coarse-to-fine grid optimization strategy to significantly reduce computation time. Comprehensive evaluations on simulated data and real experimental images (microtubules, endoplasmic reticulum, Escherichia coli, etc.) demonstrate that GEOREC achieves high-fidelity and efficient super-resolution reconstruction and outperforms the state-of-the-art deconvolution methods.

A PCA Model for Surface Reconstruction from Point Clouds

Hao Liu Hong Kong Baptist University Hong Kong Co-Author(s):

Abstract: Point cloud data represents a crucial category of information for mathematical modeling, and surface reconstruction from such data is an important task across various disciplines. In this presentation, we present our recent works for surface reconstruction from point cloud data. Our model utilizes a mean curvature term as regularizer. When the data are incomplete or noisy, a Principal Component Analysis (PCA) based variational model is proposed. Initially, we employ PCA to estimate the normal information of the underlying surface from the available point cloud data. This estimated normal information serves as a regularizer in our model, guiding the reconstruction of the surface, particularly in areas with missing data. An operator-splitting method is designed to effectively solve the proposed model. Through systematic experimentation, we demonstrate that our model is robust to noise, and successfully infers surface structures in data-missing regions and well reconstructs the underlying surfaces, outperforming existing methodologies.

Learned Spherical ADMM for Rician Noise Removal

Zhifang Liu Tianjin Normal University Peoples Rep of China Co-Author(s):

Abstract: In this talk, we introduce a novel method called the learned spherical alternating direction method of multipliers (LSADMM). This method is designed to effectively remove Rician noise under spherical constraints. LSADMM unfolds the iterations of a proximal linearized ADMM solver into a deep neural network. The solver is originally used for a sphere-constrained variational model. The network alternates between lightweight, learnable gradient-descent modules and fixed, physics-based operators. Extensive numerical experiments are conducted on both synthetic and real-world datasets. The results show that LSADMM achieves competitive restoration performance. Its architecture is lightweight and requires substantially fewer parameters than conventional end-to-end deep learning methods.

Accelerating Imaging Inverse Problems with Data Sampling and Proximal Skipping

Evangelos Papoutsellis Finden Ltd, University of Manchester England Co-Author(s):

Abstract: Large-scale imaging inverse problems are often limited by two expensive operations repeated at every iteration: gradient updates for the data-fidelity term and proximal evaluations for the regulariser. In this talk, we show how randomized proximal skipping and data splitting can substantially reduce this cost without sacrificing reconstruction quality. Numerical results on synthetic and real tomographic datasets demonstrate substantial runtime reductions, with speed-ups of 5x to 20x compared with standard approaches, while maintaining high-quality reconstructions.

A Tunable Despeckling Neural Network Stabilized via Diffusion Equation

Yi Ran Harbin Institute of Technology Peoples Rep of China Co-Author(s):

Abstract: The removal of multiplicative Gamma noise is a critical research area in the application of synthetic aperture radar (SAR) imaging, where neural networks serve as a potent tool. However, real-world data often diverges from theoretical models, exhibiting various disturbances, which makes the neural network less effective. Adversarial attacks can be used as a criterion for judging the adaptability of neural networks to real data, since they can find the most extreme perturbations that make neural networks ineffective. In this work, we propose a tunable, regularized neural network framework that unrolls a shallow neural denoising block and a diffusion regularization block into a single network for end-to-end training. The linear heat equation, known for its inherent smoothness and low-pass filtering properties, is adopted as the diffusion regularization block. The smoothness of our outputs is controlled by a single time step hyperparameter that can be adjusted dynamically. The stability and convergence of our model are theoretically proven. Experimental results demonstrate that the proposed model effectively eliminates high-frequency oscillations induced by adversarial attacks. Finally, the proposed model is benchmarked against several state-of-the-art denoising methods on simulated images, adversarial samples, and real SAR images, achieving superior performance in both quantitative and visual evaluations.

Continuum limit of p-biharmonic equations on graphs

Kehan Shi China Jiliang university Peoples Rep of China Co-Author(s):    Martin Burger

Abstract: This talk considers the $p$-biharmonic equation on graphs, which arises in point cloud processing and can be interpreted as a natural extension of the graph $p$-Laplacian from the perspective of hypergraphs. The asymptotic behavior of the solution is discussed for the random geometric graph when the number of data points goes to infinity. We show that the continuum limit is an appropriately weighted $p$-biharmonic equation with homogeneous Neumann boundary conditions. The result relies on the uniform $L^p$ estimates for solutions and gradients of nonlocal and graph Poisson equations.

A Damped Second-Order Flow for High-Order Segmentation Models with Efficient SAV Schemes

Shengzhu Shi Harbin Institute of Technology Peoples Rep of China Co-Author(s):

Abstract: Traditional variational segmentation models are typically solved by deriving the corresponding gradient flow, which evolves the level set function along the steepest descent direction toward a stationary point. While such first-order flows often suffer from slow convergence and sensitivity to initialization, frequently becoming trapped in local minima. In recent years, damped second-order gradient flows have gained attention for their ability to accelerate convergence through inertial dynamics. In this paper, we investigate a damped second-order gradient flow for a class of high-order variational segmentation models. By incorporating a damping mechanism, the proposed flow achieves significantly accelerated convergence to stationary points compared to standard first-order methods. To address numerical challenges arising from nonlinearity and high-order derivatives, we develop efficient, unconditionally energy-stable schemes based on the scalar auxiliary variable method and its variants, ensuring long-time stability without restrictive time step constraints. Extensive experiments demonstrate that the proposed method not only accelerates convergence substantially but also exhibits improved robustness against initialization, effectively alleviating the local minima issue inherent in traditional level set approaches.

COFM:Physics-Informed Design of Input Convex Neural Networks for Consistency Optimal Transport Flow Matching

Fanghui Song Harbin Institute of Technology Peoples Rep of China Co-Author(s):

Abstract: We propose a consistency model based on the optimal-transport flow. A physics-informed design of partially input-convex neural networks (PICNN) plays a central role in constructing the flow field that emulates the displacement interpolation. During the training stage, we couple the Hamilton Jacobi (HJ) residual in the OT formulation with the original flow matching loss function. Our approach avoids inner optimization subproblems that are present in previous one-step OFM approaches. During the prediction stage, our approach supports both one-step (Brenier-map) and multi-step ODE sampling from the same learned potential, leveraging the straightness of the OT flow. We validate scalability and performance on standard OT benchmarks.

An Effective Level Set Method With Molecular Beam Epitaxy Regularization for Color-Texture Image Segmentation

Jiebao Sun Harbin Institute of Technology Peoples Rep of China Co-Author(s):

Abstract: We propose a novel variational model for color-texture image segmentation by embedding the molecular beam epitaxy (MBE) equation into a multi-cue segmentation (MCS) framework. The MBE equation incorporates a fourth-order diffusion term to smooth high-frequency noise while preserving curvature variations, along with a non-equilibrium term to ensure mass conservation and suppress oscillations, thereby eliminating the need for frequent reinitialization. Inspired by the physical principles of crystal film growth, this approach regulates the level set evolution by controlling thin-film growth dynamics, improving both stability and accuracy. We derive the gradient flow equation of the proposed model and prove the existence of a weak solution using the Galerkin approximation method. To solve the model efficiently, we design an implicit-explicit (IMEX) scheme, and employ an additive operator splitting (AOS) method to obtain the diffusion tensor. Extensive experiments demonstrate that the MBE-MCS model achieves more stable level set evolutions, better preserves fine structural details, and delivers superior segmentation accuracy, even for images with noise, sharp corners, and complex backgrounds.

A primal-dual splitting algorithm for monotone inclusions with applications

Yuchao Tang Guangzhou University Peoples Rep of China Co-Author(s):    Yuchao Tang

Abstract: In this paper, we study a broad class of structured monotone inclusion problems in real Hilbert spaces. We propose a novel primal dual splitting algorithm for solving such inclusions, which accommodates multiple monotone operators, cocoercive terms, and composite monotone operators involving linear mappings. The algorithm combines forward evaluations for the cocoercive components with backward steps for the monotone operators, and incorporates a dual update to handle the linear composition term. Our framework generalizes and unifies several existing methods, while requiring only a single resolvent or operator evaluation per iteration, thereby maintaining computational efficiency. We establish weak convergence of the generated iterates under standard assumptions on monotonicity and cocoercivity. Furthermore, strong convergence is guaranteed under a mild regularity condition, such as uniform monotonicity. Finally, we present numerical experiments on structured convex and nonconvex optimization problems arising in image deblurring and denoising, which demonstrate the practical efficiency and flexibility of the proposed approach.

Learnable Mixture Distribution Prior for Image Denoising

Faqiang Wang Beijing Normal University Peoples Rep of China Co-Author(s):    Zhuoxiao Li, Li Cui, Jun Liu, Haiyang Huang

Abstract: In variational-based image denoising, the regularizer derived from mixture distributions plays a crucial role in preserving image details. However, this type of mixture distribution priors has not been incorporated into deep learning-based denoising methods. In this talk, we give a method for learning regularizers based on a learnable Laplacian mixture distribution for image denoising. Our approach is motivated by the assumption that deep image features follow a latent distribution with a mixture model. To address this assumption, we propose a regularizer with learnable weights by considering the dual problem of maximum likelihood estimation for the deep features. The dual variable in this problem represents an attention weight, which can be learned using a numerical scheme with an unrolling technique. Notably, our method establishes a connection between the mixture distribution prior and the popular attention mechanism in deep learning. The results demonstrate the superior performance of our approach for image denoising.

Pediatric Disease Diagnosis Based on Multimodal Data Fusion

Yan Wang Chongqing Normal University Peoples Rep of China Co-Author(s):

Abstract: This report will present some research progress of the research group in the field of pediatric disease diagnosis. In the diagnosis of abnormal conditions in children`s lungs based on multimodal AI, the abnormal detection technology based on AE-FLOW and the medical image-text interaction platform will be introduced, and the clinical application of this topic will be discussed; In the work of brain cognition and rehabilitation for children with hyperactivity disorder, the research platform of the topic, database construction, and research on children`s hyperactivity disorder based on brain functional imaging will be presented.

Identifying the order and a space source term in a time fractional diffusion-wave equation

Ting Wei Lanzhou University Peoples Rep of China Co-Author(s):    Ting Wei, Jianming Xu, Xi Yue

Abstract: I will talk an inverse problem for identifying the order of time fractional derivative and a space-dependent source term in a time fractional diffusion-wave equation from some additional measured data in a subdomain or on a with a small time period. The Lipschitz continuity of forward operators mapping the unknown order and source term into the given data are established based on the stability estimates of solution for the direct problem. We prove the uniqueness of the considered inverse problems by using the asymptotic behavior of the solution at $t=0$ , the Titchmarsh convolution theorem and the Duhamel principle. Moreover, a Tikhonov-type regularization method is proposed with $H^1$-norm as a penalty term. The existence of the regularized solution and its convergence to the exact solution under a suitable regularization parameter choice are obtained. Then we employ a linearized iteration algorithm combined with the piecewise linear finite element approximation to find simultaneously the approximate order and space source term. Three numerical examples for one- and two-dimensional cases are tested and the numerical results demonstrate the effectiveness of the proposed method.

Stable Recovery Guarantees for Blind Deconvolution under Random Mask Assumption

Yu Xia Hangzhou Normal University Peoples Rep of China Co-Author(s):

Abstract: This study addresses the blind deconvolution problem with modulated inputs, focusing on a measurement model where an unknown blurring kernel is convolved with multiple random modulations (coded masks) of a signal, subject to l2-bounded noise. We introduce a more generalized framework for coded masks, enhancing the versatility of our approach. Our work begins within a constrained least squares framework, where we establish a robust recovery bound for both kernel h and signal x, demonstrating its near-optimality up to a logarithmic factor. Additionally, we present a new recovery scheme that leverages sparsity constraints on x. This approach significantly reduces the sampling complexity to the order of L=O(log n) when the non-zero elements of x are sufficiently separated. Furthermore, we demonstrate that incorporating sparsity constraints yields a refined error bound compared to the traditional constrained least squares model. The proposed method results in more robust and precise signal recovery, as evidenced by both theoretical analysis and numerical simulations. These findings contribute to advancing the field of blind deconvolution and offer potential improvements in various applications requiring signal reconstruction from modulated inputs.

A Physical-Model and Data-Driven Diffusion Method for PET/MRI Imaging

Taofeng Xie Inner Mongolia Medical University Peoples Rep of China Co-Author(s):    Chentao Cao, Zhuoxu Cui, Yu Guo, Caiying Wu, Xuemei Wang, Qingneng Li, Zhanli Hu, Tao Sun, Ziru Sang, Yihang Zhuo, Yanjie Zhu, Dong Liang, Qiyu Jin, Hongwu Zeng, Guoqing Chen, Haifeng Wang

Abstract: PET/MRI provides critical multimodal information for diagnosing diseases like Alzheimer`s. However, PET imaging faces challenges such as high costs, limited availability, and radiation risks from tracers. This report presents a novel framework that combines physical imaging models with data-driven diffusion models to improve PET/MRI accessibility and safety. We first propose an MRI-guided PET generation method based on Score-based Generative Models and Stochastic Differential Equations. This approach uses structural priors from MRI to synthesize high-quality PET images. Furthermore, we introduce a joint reconstruction method that integrates the Poisson noise characteristics of PET with the Gaussian noise of MRI. Experimental results across different magnetic field strengths demonstrate that our method significantly outperforms traditional GAN-based approaches in terms of signal-to-noise ratio and clinical accuracy. This research provides a robust technical path for low-dose, high-efficiency clinical imaging.

An accelerated operator splitting algorithm for Euler`s elastic-based image models

Yunhua XUE Nankai University Peoples Rep of China Co-Author(s):    Haibin Su and Chunlin Wu

Abstract: We present an efficient numerical algorithm for solving the Euler elastic-based model in image inpainting and segmentation. These models involve a nonsmooth, nonconvex curvature term, which presents numerical challenges. We develop an acclerated operator splitting algorithm. This algorithm is obtained by introducing the inertial extrapolation technique into the operator-splitting algorithm based on th Lie scheme and Marchuk-Yanenko discretization. We also present numerical experiments on inpainting and segmentation problems by the algorithm. These tests demonstrate the effectiveness and efficiency, especially the remarkable superiority in terms of iteration number and running time.

Topological Fingerprints of Tabular Surfaces in images Based on Persistent Homology

Xiaoping Yang Nanjing University Peoples Rep of China Co-Author(s):

Abstract: Persistent homology is a crucial tool in topological data analysis (TDA), and the key to its applications lies in constructing a suitable finite-length ascending sequence of simplicial complexes (i.e., a filtration). Unlike most other approaches that directly apply persistence diagrams to downstream tasks, our core insight is that changes in the topological structure of simplicial complexes within a filtration are necessarily driven by specific vertices. We thus propose the concept of homology-generating/vanishing critical points, which aims to locate the vertices in the original data that induce topological changes in images. Subsequently, taking a novel geodesic filtration as an example, we investigate the relationships between 0-dim, 1-dim, and 2-dim PH points in persistence diagrams and the vertices in tubular structures of images. Experiments conducted on multiple datasets demonstrate that our method can accurately locate the homology-generating/vanishing critical points (e.g., branch points, endpoints, adhesions, etc.) and exhibits significant applications potential in relevant fields.

A time-fractional equation with the gray level indicator for image multiplicative noise removal

Wenjuan Yao Harbin Institute of Technology Peoples Rep of China Co-Author(s):

Abstract: Synthetic aperture radar (SAR) images suffer from multiplicative noise, which significantly degrades their quality and visual effect. In this work, we propose a time-fractional equation with a gray level indicator for SAR image denoising. By introducing the time-fractional derivative, the model effectively interpolates between the heat and wave equations, preserving valuable information in highly oscillatory regions. Moreover, the fractional-order derivative operator possesses nonlocal properties, allowing for the inclusion of information from nonlocal domains. In order to achieve better control over the diffusion process, we incorporate a gray level indicator into the diffusion coefficients of our model, which allows us to fully take into account the gray level information of the image. We also investigate the well-posedness of the proposed model. Experiments on natural and real SAR images demonstrate the superiority of our method in removing multiplicative noise, particularly in highly oscillatory regions and texture-rich images.

Hierarchical Exact Solver for Large-scale Optimal Transport and its applciations

Xiaoqun Zhang Shanghai Jiao Tong University Peoples Rep of China Co-Author(s):    Wenzhou Xia, Jingwei Liang, Qiaoqiao Ding

Abstract: Optimal transport (OT) underlies many machine-learning and computer-vision tasks, yet solving large-scale OT problems under a tight memory budget remains challenging because of an inherent trilemma among precision, memory efficiency and dimensional scalability. To resolve this trade-off we propose a memory-efficient, dimension-scalable hierarchical exact solver for large-scale OT with low-rank cost. The proposed algorithm is a multi-resolution decomposition of the OT problem coupled with parallel-friendly linear-programming solvers. To guarantee memory efficiency we strictly bound the storage to linear complexity via active support pruning. Theoretically, we prove a scale-independent iteration-complexity upper bound for the refinement phase (consistent with the empirical observation) and show that, under standard assumptions, the algorithm converges to the global optimum. Numerical experiments demonstrate the scalability and exactness of the proposed algorithm across a wide range of regimes. The algorithm is capable to handle million-scale problems in very high dimensions (n=106, d=8192) on a single GPU, while still delivering exact solutions on synthetic high-dimensional data. The method thus alleviates the memory and scalability bottlenecks of existing solvers and resolves the precision-memory-dimensionality trilemma for large-scale OT.