SIAM Journal on Imaging Sciences最新文献

{"title":"Fast Rigid Alignment of Heterogeneous Images in Sliced Wasserstein Distance.","authors":"Yunpeng Shi, Amit Singer, Eric J Verbeke","doi":"10.1137/25m1742916","DOIUrl":"10.1137/25m1742916","url":null,"abstract":"<p><p>Many applications of computer vision rely on the alignment of similar but nonidentical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier methods with the robustness of sliced probability metrics and allows us to efficiently compute the alignment between two <math><mi>L</mi> <mo>×</mo> <mi>L</mi></math> images using the sliced 2-Wasserstein distance in <math><mi>𝒪</mi> <mfenced> <mrow> <msup><mrow><mi>L</mi></mrow> <mrow><mn>2</mn></mrow> </msup> <mspace></mspace> <mtext>log</mtext> <mspace></mspace> <mi>L</mi></mrow> </mfenced> </math> operations. We show that our method is robust to translations, rotations, and deformations in the images.</p>","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"19 3","pages":"1469-1515"},"PeriodicalIF":2.5,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13459015/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148714256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Smooth optimization using global and local low-rank regularizers.","authors":"Rodrigo A Lobos, Javier Salazar Cavazos, Raj Rao Nadakuditi, Jeffrey A Fessler","doi":"10.1137/25m175891x","DOIUrl":"10.1137/25m175891x","url":null,"abstract":"<p><p>Many inverse problems and signal processing problems involve low-rank regularizers based on the nuclear norm. Commonly, proximal gradient methods (PGM) are adopted to solve this type of non-smooth problems as they can offer fast and guaranteed convergence. However, PGM methods cannot be simply applied in settings where low-rank models are imposed locally on overlapping patches; therefore, heuristic approaches have been proposed that lack convergence guarantees. In this work we propose to replace the nuclear norm with a smooth approximation in which a Huber-type function is applied to each singular value. By providing a theoretical framework based on singular value function theory, we show that important properties can be established for the proposed regularizer, such as: convexity, differentiability, and Lipschitz continuity of the gradient. Moreover, we provide a closed-form expression for the regularizer gradient, enabling the use of standard iterative gradient-based optimization algorithms (<i>e.g.</i>, nonlinear conjugate gradient) that can easily address the case of overlapping patches and have well-known convergence guarantees. In addition, we provide a novel step-size selection strategy based on a quadratic majorizer of the line-search function that leverages the Huber characteristics of the proposed regularizer. Finally, we assess the proposed optimization framework by providing empirical results in dynamic magnetic resonance imaging (MRI) reconstruction in the context of local low-rank models with overlapping patches.</p>","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"19 2","pages":"839-878"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13138729/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147845159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subspace Method of Moments for <i>Ab Initio</i> 3-D Single Particle Cryo-EM Reconstruction.","authors":"Jeremy Hoskins, Yuehaw Khoo, Oscar Mickelin, Amit Singer, Yuguan Wang","doi":"10.1137/24m1699644","DOIUrl":"10.1137/24m1699644","url":null,"abstract":"<p><p>Cryo-electron microscopy (cryo-EM) is a widely used technique for recovering the three-dimensional (3-D) structure of biological molecules from a large number of experimentally generated noisy 2-D tomographic projection images of the 3-D structure, taken from unknown viewing angles. Through computationally intensive algorithms, these observed images are processed to reconstruct the 3-D structures. Many popular computational methods rely on estimating the unknown angles as part of the reconstruction process, which becomes particularly challenging at low signal-to-noise ratios. The method of moments offers an alternative approach that circumvents the estimation of viewing orientations of individual projection images by instead estimating the underlying distribution of the viewing angles, and is robust to noise given sufficiently many images. However, the method of moments typically entails computing higher-order moments of the projection images, incurring significant computational and memory costs. To mitigate this, we propose a new approach called the subspace method of moments (SubspaceMoM), which compresses the first three moments using data-driven low-rank tensor techniques as well as expansion into a suitable function basis. The compressed moments can be efficiently computed from the set of projection images using numerical quadrature and can be employed to jointly reconstruct the 3-D structure and the distribution of viewing orientations. We illustrate the practical applicability of SubspaceMoM through numerical experiments using up to the third-order moment on synthetic datasets with a simplified cryo-EM image formation model, which significantly improves the reconstruction resolution compared to previous MoM approaches.</p>","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"19 1","pages":"364-409"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13221091/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148139593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations","authors":"Sven Dummer, Nicola Strisciuglio, Christoph Brüne","doi":"10.1137/24m1644730","DOIUrl":"https://doi.org/10.1137/24m1644730","url":null,"abstract":"Diffeomorphic registration frameworks such as large deformation diffeomorphic metric mapping(LDDMM) are used in computer graphics and the medical domain for atlas building, statisticallatent modeling, and pairwise and groupwise registration. In recent years, researchers have devel-oped neural network--based approaches regarding diffeomorphic registration to improve the accuracyand computational efficiency of traditional methods. In this work, we focus on a limitation of neu-ral network--based atlas building and statistical latent modeling methods, namely that they either(i) are resolution dependent or (ii) disregard any data- or problem-specific geometry needed forproper mean-variance analysis. In particular, we overcome this limitation by designing a novel en-coder based on resolution-independent implicit neural representations. The encoder achieves res-olution invariance for LDDMM-based statistical latent modeling. Additionally, the encoder addsLDDMM Riemannian geometry to resolution-independent deep learning models for statistical la-tent modeling. We investigate how the Riemannian geometry improves latent modeling and isrequired for a proper mean-variance analysis. To highlight the benefit of resolution independence forLDDMM-based data variability modeling, we show that our approach outperforms current neuralnetwork--based LDDMM latent code models. Our work paves the way for more research into howRiemannian geometry; shape, respectively, image analysis; and deep learning can be combined.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"17 4","pages":"2302-2330"},"PeriodicalIF":0.0,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ris.utwente.nl/ws/files/471618290/2305.12854.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147918576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniform Recovery Guarantees for Quantized Corrupted Sensing Using Structured or Generative Priors","authors":"Junren Chen, Zhaoqiang Liu, Meng Ding, Michael K. Ng","doi":"10.1137/23m1578358","DOIUrl":"https://doi.org/10.1137/23m1578358","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1909-1977, September 2024. <br/> Abstract.This paper studies quantized corrupted sensing where the measurements are contaminated by unknown corruption and then quantized by a dithered uniform quantizer. We establish uniform guarantees for Lasso that ensure the accurate recovery of all signals and corruptions using a single draw of the sub-Gaussian sensing matrix and uniform dither. For signal and corruption with structured priors (e.g., sparsity, low-rankness), our uniform error rate for constrained Lasso typically coincides with the nonuniform one up to logarithmic factors, indicating that the uniformity costs very little. By contrast, our uniform error rate for unconstrained Lasso exhibits worse dependence on the structured parameters due to regularization parameters larger than the ones for nonuniform recovery. These results complement the nonuniform ones recently obtained in Sun, Cui, and Liu [IEEE Trans. Signal Process., 70 (2022), pp. 600–615] and provide more insights for understanding actual applications where the sensing ensemble is typically fixed and the corruption may be adversarial. For signal and corruption living in the ranges of some Lipschitz continuous generative models (referred to as generative priors), we achieve uniform recovery via constrained Lasso with a measurement number proportional to the latent dimensions of the generative models. We present experimental results to corroborate our theories. From the technical side, our treatments to the two kinds of priors are (nearly) unified and share the common key ingredients of a (global) quantized product embedding (QPE) property, which states that the dithered uniform quantization (universally) preserves the inner product. As a by-product, our QPE result refines the one in Xu and Jacques [Inf. Inference, 9 (2020), pp. 543–586] under the sub-Gaussian random matrix, and in this specific instance, we are able to sharpen the uniform error decaying rate (for the projected back-projection estimator with signals in some convex symmetric set) presented therein from [math] to [math].","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"35 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Restoration Guarantee of Image Inpainting via Low Rank Patch Matrix Completion","authors":"Jian-Feng Cai, Jae Kyu Choi, Jingyang Li, Guojian Yin","doi":"10.1137/23m1614456","DOIUrl":"https://doi.org/10.1137/23m1614456","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1879-1908, September 2024. <br/> Abstract.In recent years, patch-based image restoration approaches have demonstrated superior performance compared to conventional variational methods. This paper delves into the mathematical foundations underlying patch-based image restoration methods, with a specific focus on establishing restoration guarantees for patch-based image inpainting, leveraging the assumption of self-similarity among patches. To accomplish this, we present a reformulation of the image inpainting problem as structured low-rank matrix completion, accomplished by grouping image patches with potential overlaps. By making certain incoherence assumptions, we establish a restoration guarantee, given that the number of samples exceeds the order of [math], where [math] denotes the size of the image and [math] represents the sum of ranks for each group of image patches. Through our rigorous mathematical analysis, we provide valuable insights into the theoretical foundations of patch-based image restoration methods, shedding light on their efficacy and offering guidelines for practical implementation.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"5 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inclusion and Estimates for the Jumps of Minimizers in Variational Denoising","authors":"Antonin Chambolle, Michał Łasica","doi":"10.1137/23m1627948","DOIUrl":"https://doi.org/10.1137/23m1627948","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1844-1878, September 2024. <br/> Abstract.We study stability and inclusion of the jump set of minimizers of convex denoising functionals, such as the celebrated “Rudin–Osher–Fatemi” functional, for scalar or vectorial signals. We show that under mild regularity assumptions on the data fidelity term and the regularizer, the jump set of the minimizer is essentially a subset of the original jump set. Moreover, we give an estimate on the magnitude of the jumps in terms of the data. This extends old results, in particular of the first author (with Caselles and Novaga) and of Valkonen, to much more general cases. We also consider the case where the original datum has unbounded variation, and we define a notion of its jump set which, again, must contain the jump set of the solution.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"7 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Removing the Mask—Reconstructing a Real-Valued Field on the Sphere from a Masked Field by Spherical Fourier Analysis","authors":"Jan Hamann, Quoc T. Le Gia, Ian H. Sloan, Robert S. Womersley","doi":"10.1137/23m1603157","DOIUrl":"https://doi.org/10.1137/23m1603157","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1820-1843, September 2024. <br/> Abstract.The paper analyzes a spectral approach to reconstructing a scalar field on the sphere, given only information about a masked version of the field, together with precise information about the (smooth) mask. The theory is developed for a general mask and later specialized to the case of an axially symmetric mask. Numerical experiments are given for the case of an axial mask motivated by the cosmic microwave background, assuming that the underlying field is a realization of a Gaussian random field with an artificial angular power spectrum of moderate degree ([math]). The recovery is highly satisfactory in the absence of noise and even in the presence of moderate noise.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"6 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"TILT: Topological Interface Recovery in Limited-Angle Tomography","authors":"Elli Karvonen, Matti Lassas, Pekka Pankka, Samuli Siltanen","doi":"10.1137/23m1611567","DOIUrl":"https://doi.org/10.1137/23m1611567","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1761-1794, September 2024. <br/> Abstract.A novel reconstruction method is introduced for the severely ill-posed inverse problem of limited-angle tomography. It is well known that, depending on the available measurement, angles specify a subset of the wavefront set of the unknown target, while some oriented singularities remain invisible in the data. Topological Interface recovery for Limited-angle Tomography, or TILT, is based on lifting the visible part of the wavefront set under a universal covering map. In the space provided, it is possible to connect the appropriate pieces of the lifted wavefront set correctly using dual-tree complex wavelets, a dedicated metric, and persistent homology. The result is not only a suggested invisible boundary but also a computational representation for all interfaces in the target.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Inexact Majorized Proximal Alternating Direction Method of Multipliers for Diffusion Tensors","authors":"Hong Zhu, Michael K. Ng","doi":"10.1137/23m1607015","DOIUrl":"https://doi.org/10.1137/23m1607015","url":null,"abstract":"SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1795-1819, September 2024. <br/> Abstract.This paper focuses on studying the denoising problem for positive semidefinite fourth-order tensor field estimation from noisy observations. The positive semidefiniteness of the tensor is preserved by mapping the tensor to a 6-by-6 symmetric positive semidefinite matrix where its matrix rank is less than or equal to three. For denoising, we propose to use an anisotropic discrete total variation function over the tensor field as the regularization term. We propose an inexact majorized proximal alternating direction method of multipliers for such a nonconvex and nonsmooth optimization problem. We show that an [math]-stationary solution of the resulting optimization problem can be found in no more than [math] iterations. The effectiveness of the proposed model and algorithm is tested using multifiber diffusion weighted imaging data, and our numerical results demonstrate that our method outperforms existing methods in terms of denoising performance.","PeriodicalId":49528,"journal":{"name":"SIAM Journal on Imaging Sciences","volume":"39 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}