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Polarimetric Fourier Phase Retrieval SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-03-11 Julien Flamant, Konstantin Usevich, Marianne Clausel, David Brie
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 632-671, March 2024. Abstract. This work introduces polarimetric Fourier phase retrieval (PPR), a physically inspired model to leverage polarization of light information in Fourier phase retrieval problems. We provide a complete characterization of its uniqueness properties by unraveling equivalencies with two related problems, namely, bivariate
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PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-03-07 Xue-Cheng Tai, Hao Liu, Raymond Chan
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 540-594, March 2024. Abstract. For problems in image processing and many other fields, a large class of effective neural networks has encoder-decoder-based architectures. Although these networks have shown impressive performance, mathematical explanations of their architectures are still underdeveloped. In this paper, we study the encoder-decoder-based
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Numerical Implementation of Generalized V-Line Transforms on 2D Vector Fields and their Inversions SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-03-07 Gaik Ambartsoumian, Mohammad J. Latifi Jebelli, Rohit K. Mishra
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 595-631, March 2024. Abstract.The paper discusses numerical implementations of various inversion schemes for generalized V-line transforms on vector fields introduced in [G. Ambartsoumian, M. J. Latifi, and R. K. Mishra, Inverse Problems, 36 (2020), 104002]. It demonstrates the possibility of efficient recovery of an unknown vector field from
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A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry Applied to Imaging SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-03-05 Qiguang Chen, Zhiwen Li, Lok Ming Lui
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 501-539, March 2024. Abstract. Many imaging problems can be formulated as mapping problems. A general mapping problem aims to obtain an optimal mapping that minimizes an energy functional subject to the given constraints. Existing methods to solve the mapping problems are often inefficient and can sometimes get trapped in local minima. An extra
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Fractional Fourier Transforms Meet Riesz Potentials and Image Processing SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-02-27 Zunwei Fu, Yan Lin, Dachun Yang, Shuhui Yang
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 476-500, March 2024. Abstract.Via chirp functions from fractional Fourier transforms, we introduce fractional Riesz potentials related to chirp functions, which are further used to give a new image encryption method with double phase coding. In a comparison with the image encryption method based on fractional Fourier transforms, via a series
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Learnable Nonlocal Self-Similarity of Deep Features for Image Denoising SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-02-23 Junying Meng, Faqiang Wang, Jun Liu
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 441-475, March 2024. Abstract. High-dimensional deep features extracted by convolutional neural networks have nonlocal self-similarity. However, incorporating this nonlocal prior of deep features into deep network architectures with an interpretable variational framework is rarely explored. In this paper, we propose a learnable nonlocal self-similarity
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Analysis of View Aliasing for the Generalized Radon Transform in [math] SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-02-23 Alexander Katsevich
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 415-440, March 2024. Abstract. In this paper we consider the generalized Radon transform [math] in the plane. Let [math] be a piecewise smooth function, which has a jump across a smooth curve [math]. We obtain a formula, which accurately describes view aliasing artifacts away from [math] when [math] is reconstructed from the data [math] discretized
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The Cortical V1 Transform as a Heterogeneous Poisson Problem SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-02-21 Alessandro Sarti, Mattia Galeotti, Giovanna Citti
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 389-414, March 2024. Abstract. Receptive profiles of the primary visual cortex (V1) cortical cells are very heterogeneous and act by differentiating the stimulus image as operators changing from point to point. In this paper we aim to show that the distribution of cells in V1, although not complete to reconstruct the original image, is sufficient
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The [math]-Laplace “Signature” for Quasilinear Inverse Problems SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-02-15 Antonio Corbo Esposito, Luisa Faella, Gianpaolo Piscitelli, Vincenzo Mottola, Ravi Prakash, Antonello Tamburrino
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 351-388, March 2024. Abstract. This paper refers to an imaging problem in the presence of nonlinear materials. Specifically, the problem we address falls within the framework of Electrical Resistance Tomography and involves two different materials, one or both of which are nonlinear. Tomography with nonlinear materials is in the early stages
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Reduced Order Modeling Inversion of Monostatic Data in a Multi-scattering Environment SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-02-08 Vladimir Druskin, Shari Moskow, Mikhail Zaslavsky
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 334-350, March 2024. Abstract.Data-driven reduced order models (ROMs) have recently emerged as an efficient tool for the solution of inverse scattering problems with applications to seismic and sonar imaging. One requirement of this approach is that it uses the full square multiple-input/multiple-output (MIMO) matrix-valued transfer function
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Posterior-Variance–Based Error Quantification for Inverse Problems in Imaging SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-02-07 Dominik Narnhofer, Andreas Habring, Martin Holler, Thomas Pock
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 301-333, March 2024. Abstract.In this work, a method for obtaining pixelwise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal prediction in order to obtain coverage guarantees for the error bounds, without
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A Majorization-Minimization Algorithm for Neuroimage Registration SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-02-05 Gaiting Zhou, Daniel Tward, Kenneth Lange
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 273-300, March 2024. Abstract. Intensity-based image registration is critical for neuroimaging tasks, such as 3D reconstruction, times-series alignment, and common coordinate mapping. The gradient-based optimization methods commonly used to solve this problem require a careful selection of step-length. This limitation imposes substantial time
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Image Segmentation Using Bayesian Inference for Convex Variant Mumford–Shah Variational Model SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-01-30 Xu Xiao, Youwei Wen, Raymond Chan, Tieyong Zeng
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 248-272, March 2024. Abstract. The Mumford–Shah model is a classical segmentation model, but its objective function is nonconvex. The smoothing and thresholding (SaT) approach is a convex variant of the Mumford–Shah model, which seeks a smoothed approximation solution to the Mumford–Shah model. The SaT approach separates the segmentation into
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Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruptions SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-01-25 HanQin Cai, Zehan Chao, Longxiu Huang, Deanna Needell
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 225-247, March 2024. Abstract. We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis, which aims to split the given tensor into an underlying low-rank component and a sparse outlier component. This work proposes a fast algorithm, called robust tensor CUR
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Direct Imaging Methods for Reconstructing a Locally Rough Interface from Phaseless Total-Field Data or Phased Far-Field Data SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-01-24 Long Li, Jiansheng Yang, Bo Zhang, Haiwen Zhang
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 188-224, March 2024. Abstract. This paper is concerned with the problem of inverse scattering of time-harmonic acoustic plane waves by a two-layered medium with a locally rough interface in two dimensions. A direct imaging method is proposed to reconstruct the locally rough interface from the phaseless total-field data measured on the upper
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Conductivity Imaging from Internal Measurements with Mixed Least-Squares Deep Neural Networks SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-01-23 Bangti Jin, Xiyao Li, Qimeng Quan, Zhi Zhou
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 147-187, March 2024. Abstract. In this work, we develop a novel approach using deep neural networks (DNNs) to reconstruct the conductivity distribution in elliptic problems from one measurement of the solution over the whole domain. The approach is based on a mixed reformulation of the governing equation and utilizes the standard least-squares
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Polynomial Preconditioners for Regularized Linear Inverse Problems SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-01-22 Siddharth S. Iyer, Frank Ong, Xiaozhi Cao, Congyu Liao, Luca Daniel, Jonathan I. Tamir, Kawin Setsompop
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 116-146, March 2024. Abstract. This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal operator derived from the linear operator. The preconditioner does not
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Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-01-18 Alexis Goujon, Sebastian Neumayer, Michael Unser
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 91-115, March 2024. Abstract.We propose to learn non-convex regularizers with a prescribed upper bound on their weak-convexity modulus. Such regularizers give rise to variational denoisers that minimize a convex energy. They rely on few parameters (less than 15,000) and offer a signal-processing interpretation as they mimic handcrafted sparsity-promoting
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Identification of Sparsely Representable Diffusion Parameters in Elliptic Problems SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-01-17 Luzia N. Felber, Helmut Harbrecht, Marc Schmidlin
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 61-90, March 2024. Abstract. We consider the task of estimating the unknown diffusion parameter in an elliptic PDE as a model problem to develop and test the effectiveness and robustness to noise of reconstruction schemes with sparsity regularization. To this end, the model problem is recast as a nonlinear infinite dimensional optimization
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Learning Sparsity-Promoting Regularizers Using Bilevel Optimization SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-01-10 Avrajit Ghosh, Michael McCann, Madeline Mitchell, Saiprasad Ravishankar
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 31-60, March 2024. Abstract. We present a gradient-based heuristic method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators underlying these regularizers are usually either
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A Variational Model for Nonuniform Low-Light Image Enhancement SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2024-01-04 Fan Jia, Shen Mao, Xue-Cheng Tai, Tieyong Zeng
SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 1-30, March 2024. Abstract. Low-light image enhancement plays an important role in computer vision applications, which is a fundamental low-level task and can affect high-level computer vision tasks. To solve this ill-posed problem, a lot of methods have been proposed to enhance low-light images. However, their performance degrades significantly
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Self-Supervised Deep Learning for Image Reconstruction: A Langevin Monte Carlo Approach SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-11-30 Ji Li, Weixi Wang, Hui Ji
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 2247-2284, December 2023. Abstract. Deep learning has proved to be a powerful tool for solving inverse problems in imaging, and most of the related work is based on supervised learning. In many applications, collecting truth images is a challenging and costly task, and the prerequisite of having a training dataset of truth images limits its
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Learning Regularization Parameter-Maps for Variational Image Reconstruction Using Deep Neural Networks and Algorithm Unrolling SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-11-29 Andreas Kofler, Fabian Altekrüger, Fatima Antarou Ba, Christoph Kolbitsch, Evangelos Papoutsellis, David Schote, Clemens Sirotenko, Felix Frederik Zimmermann, Kostas Papafitsoros
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 2202-2246, December 2023. Abstract. We introduce a method for the fast estimation of data-adapted, spatially and temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV) minimization. The proposed approach is inspired by recent developments in algorithm unrolling using deep neural
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IFF: A Superresolution Algorithm for Multiple Measurements SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-11-27 Zetao Fei, Hai Zhang
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 2175-2201, December 2023. Abstract. We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval [math]. This problem is known to be challenging in the regime where the spacing of the sources is below the Rayleigh length [math]. In this paper, we propose a superresolution algorithm
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Transionospheric Autofocus for Synthetic Aperture Radar SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-11-20 Mikhail Gilman, Semyon V. Tsynkov
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 2144-2174, December 2023. Abstract. Turbulent fluctuations of the electron number density in the Earth’s ionosphere may hamper the performance of spaceborne synthetic aperture radar (SAR). Previously, we have quantified the extent of the possible degradation of transionospheric SAR images as it depends on the state of the ionosphere and parameters
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An Operator Theory for Analyzing the Resolution of Multi-illumination Imaging Modalities SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-11-15 Ping Liu, Habib Ammari
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 2105-2143, December 2023. Abstract. By introducing a new operator theory, we provide a unified mathematical theory for general source resolution in the multi-illumination imaging problem. Our main idea is to transform multi-illumination imaging into single-snapshot imaging with a new imaging kernel that depends on both the illumination patterns
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Spherical Framelets from Spherical Designs SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-11-14 Yuchen Xiao, Xiaosheng Zhuang
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 2072-2104, December 2023. Abstract. In this paper, we investigate in detail the structures of the variational characterization [math] of the spherical [math]-design, its gradient [math], and its Hessian [math] in terms of fast spherical harmonic transforms. Moreover, we propose solving the minimization problem of [math] using the trust-region
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The Split Gibbs Sampler Revisited: Improvements to Its Algorithmic Structure and Augmented Target Distribution SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-11-10 Marcelo Pereyra, Luis A. Vargas-Mieles, Konstantinos C. Zygalakis
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 2040-2071, December 2023. Abstract. Developing efficient Bayesian computation algorithms for imaging inverse problems is challenging due to the dimensionality involved and because Bayesian imaging models are often not smooth. Current state-of-the-art methods often address these difficulties by replacing the posterior density with a smooth approximation
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Sequential Model Correction for Nonlinear Inverse Problems SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-10-19 Arttu Arjas, Mikko J. Sillanpää, Andreas S. Hauptmann
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 2015-2039, December 2023. Abstract. Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to second-order methods that are computationally more expensive. In this work
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A Common Lines Approach for Ab Initio Modeling of Molecules with Tetrahedral and Octahedral Symmetry SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-10-18 Adi Shasha Geva, Yoel Shkolnisky
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 1978-2014, December 2023. Abstract. A main task in cryo-electron microscopy single particle reconstruction is to find a three-dimensional model of a molecule given a set of its randomly oriented and positioned projection-images. In this work, we propose an algorithm for ab initio reconstruction for molecules with tetrahedral or octahedral symmetry
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Convolutional Forward Models for X-Ray Computed Tomography SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-10-12 Kai Zhang, Alireza Entezari
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 1953-1977, December 2023. Abstract. This paper presents a framework for efficient and accurate computation of X-ray optics, a key ingredient in optimization-based computed tomography (CT) reconstruction algorithms. Based on an algebraic framework for directional convolution in image space and detector space, we construct forward models for
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A Data-Assisted Two-Stage Method for the Inverse Random Source Problem SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-10-12 Peijun Li, Ying Liang, Yuliang Wang
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 1929-1952, December 2023. Abstract. We propose a data-assisted two-stage method for solving an inverse random source problem of the Helmholtz equation. In the first stage, the regularized Kaczmarz method is employed to generate initial approximations of the mean and variance based on the mild solution of the stochastic Helmholtz equation. A
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[math] Minimization for Signal and Image Recovery SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-10-11 Limei Huo, Wengu Chen, Huanmin Ge, Michael K. Ng
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 1886-1928, December 2023. Abstract. The nonconvex optimization method has attracted increasing attention due to its excellent ability of promoting sparsity in signal processing, image restoration, and machine learning. In this paper, we consider a new minimization method [math] [math] and its applications in signal recovery and image reconstruction
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Subaperture-Based Digital Aberration Correction for Optical Coherence Tomography: A Novel Mathematical Approach SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-10-11 Simon Hubmer, Ekaterina Sherina, Ronny Ramlau, Michael Pircher, Rainer Leitgeb
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page 1857-1885, December 2023. Abstract. In this paper, we consider subaperture-based approaches for the digital aberration correction (DAC) of optical coherence tomography (OCT) images. In particular, we introduce a mathematical framework for describing this class of approaches, leading to new insights for the subaperture-correlation method. Furthermore
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Short Communication: Localized Adversarial Artifacts for Compressed Sensing MRI SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-10-10 Rima Alaifari, Giovanni S. Alberti, Tandri Gauksson
SIAM Journal on Imaging Sciences, Volume 16, Issue 4, Page SC14-SC26, December 2023. Abstract. As interest in deep neural networks (DNNs) for image reconstruction tasks grows, their reliability has been called into question [V. Antun, F. Renna, C. Poon, B. Adcock, and A. C. Hansen, Proc. Natl. Acad. Sci. USA, 117 (2020), pp. 30088–30095; N. M. Gottschling, V. Antun, B. Adcock, and A. C. Hansen, The
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Convergence Analysis of Volumetric Stretch Energy Minimization and Its Associated Optimal Mass Transport SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-09-08 Tsung-Ming Huang, Wei-Hung Liao, Wen-Wei Lin, Mei-Heng Yueh, Shing-Tung Yau
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1825-1855, September 2023. Abstract. Volumetric stretch energy has been widely applied to the computation of volume-/mass-preserving parameterizations of simply connected tetrahedral mesh models [math]. However, this approach still lacks theoretical support. In this paper, we provide a theoretical foundation for volumetric stretch energy minimization
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An Unrolled Implicit Regularization Network for Joint Image and Sensitivity Estimation in Parallel MR Imaging with Convergence Guarantee SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-09-06 Yan Yang, Yizhou Wang, Jiazhen Wang, Jian Sun, Zongben Xu
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1791-1824, September 2023. Abstract. Parallel imaging (PI), relying on multicoils to sense [math]-space data, is an effective technique to accelerate magnetic resonance imaging by exploiting spatial sensitivity coding of multiple coils, with an integrated compressive sensing (CS) technology to achieve higher acceleration. In this paper, we
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Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-29 Michael V. Klibanov, Jingzhi Li, Loc H. Nguyen, Vladimir Romanov, Zhipeng Yang
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1762-1790, September 2023. Abstract. The first globally convergent numerical method for a coefficient inverse problem for the Riemannian radiative transfer equation (RRTE) is constructed. This is a version of the so-called convexification method, which has been pursued by this research group for a number of years for some other CIPs for PDEs
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Enhanced Digital Halftoning via Weighted Sigma-Delta Modulation SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-29 Felix Krahmer, Anna Veselovska
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1727-1761, September 2023. Abstract. In this paper, we study error diffusion techniques for digital halftoning from the perspective of 1-bit [math] quantization. We introduce a method to generate [math] schemes for two-dimensional signals as a weighted combination of their one-dimensional counterparts and show that various error diffusion schemes
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Using Decoupled Features for Photorealistic Style Transfer SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-29 Trevor Canham, Adrián Martín Fernández, Marcelo Bertalmío, Javier Portilla
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1687-1726, September 2023. Abstract. In this work we propose a photorealistic style transfer method for image and video that is based on vision science principles and on a recent mathematical formulation for the deterministic decoupling of sample statistics. The novel aspects of our approach include matching decoupled moments of higher order
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Bilevel Imaging Learning Problems as Mathematical Programs with Complementarity Constraints: Reformulation and Theory SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-24 Juan Carlos De los Reyes
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1655-1686, September 2023. Abstract. We investigate a family of bilevel imaging learning problems where the lower-level instance corresponds to a convex variational model involving first- and second-order nonsmooth sparsity-based regularizers. By using geometric properties of the primal-dual reformulation of the lower-level problem and introducing
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Image Denoising: The Deep Learning Revolution and Beyond—A Survey Paper SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-24 Michael Elad, Bahjat Kawar, Gregory Vaksman
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1594-1654, September 2023. Abstract. Image denoising—removal of additive white Gaussian noise from an image—is one of the oldest and most studied problems in image processing. Extensive work over several decades has led to thousands of papers on this subject, and to many well-performing algorithms for this task. Indeed, 10 years ago, these
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The Linear Sampling Method for Random Sources SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-23 Josselin Garnier, Houssem Haddar, Hadrien Montanelli
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1572-1593, September 2023. Abstract. We present an extension of the linear sampling method for solving the sound-soft inverse acoustic scattering problem with randomly distributed point sources. The theoretical justification of our sampling method is based on the Helmholtz–Kirchhoff identity, the cross-correlation between measurements, and
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Imaging a Moving Point Source from Multifrequency Data Measured at One and Sparse Observation Directions (Part I): Far-Field Case SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-17 Hongxia Guo, Guanghui Hu, Guanqiu Ma
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1535-1571, September 2023. Abstract. We propose a multifrequency algorithm for recovering partial information on the trajectory of a moving point source from one and sparse far-field observation directions in the frequency domain. The starting and terminal time points of the moving source are both supposed to be known. We introduce the concept
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Singular Value Decomposition of the Wave Forward Operator with Radial Variable Coefficients SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-11 Minam Moon, Injo Hur, Sunghwan Moon
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1520-1534, September 2023. Abstract. Photoacoustic tomography (PAT) is a novel and promising technology in hybrid medical imaging that involves generating acoustic waves in the object of interest by stimulating electromagnetic energy. The acoustic wave is measured outside the object. One of the key mathematical problems in PAT is the reconstruction
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Topological Identification of Vortical Flow Structures in the Left Ventricle of the Heart SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-11 Takashi Sakajo, Keiichi Itatani
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1491-1519, September 2023. Abstract. Vortical blood flow structures inside the heart’s left ventricle (LV) play a crucial role in an efficient blood supply from the heart to organs. Recent medical imaging and computational technology progress have brought us blood flow visualization tools in echocardiography and cardiac MRI. However, there
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Regularizing Orientation Estimation in Cryogenic Electron Microscopy Three-Dimensional Map Refinement through Measure-Based Lifting over Riemannian Manifolds SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-10 Willem Diepeveen, Jan Lellmann, Ozan Öktem, Carola-Bibiane Schönlieb
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1440-1490, September 2023. Abstract. Motivated by the trade-off between noise robustness and data consistency for joint three-imensional (3D) map reconstruction and rotation estimation in single particle cryogenic-electron microscopy (Cryo-EM), we propose ellipsoidal support lifting (ESL), a measure-based lifting scheme for regularizing and
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Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown View Tomography SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-08 Shuai Huang, Mona Zehni, Ivan Dokmanić, Zhizhen Zhao
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1398-1439, September 2023. Abstract. Unknown view tomography (UVT) reconstructs a 3D density map from its 2D projections at unknown, random orientations. A line of work starting with Kam (1980) employs the method of moments with rotation-invariant Fourier features to solve UVT in the frequency domain, assuming that the orientations are uniformly
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A Learnable Group-Tube Transform Induced Tensor Nuclear Norm and Its Application for Tensor Completion SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-03 Ben-Zheng Li, Xi-Le Zhao, Xiongjun Zhang, Teng-Yu Ji, Xinyu Chen, Michael K. Ng
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1370-1397, September 2023. Abstract. The transform-based tensor nuclear norm (TNN) methods have shown good recovery results for tensor completion. However, the TNN methods are based on the single-tube transforms in which transforms are applied to each tube independently. The performance of the single-tube transform-based TNN methods is not
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Inversion of Band-Limited Discrete Fourier Transforms of Binary Images: Uniqueness and Algorithms SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-08-01 Howard W. Levinson, Vadim Markel, Nicholas Triantafillou
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1338-1369, September 2023. Abstract. Conventional inversion of the discrete Fourier transform (DFT) requires all DFT coefficients to be known. When the DFT coefficients of a rasterized image (represented as a matrix) are known only within a pass band, the original matrix cannot be uniquely recovered. In many cases of practical importance, the
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Image Recovery for Blind Polychromatic Ptychography SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-07-28 Frank Filbir, Oleh Melnyk
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1308-1337, September 2023. Abstract. Ptychography is a lensless imaging technique, which considers reconstruction from a set of far-field diffraction patterns obtained by illuminating small overlapping regions of the specimen. In many cases, the distribution of light inside the illuminated region is unknown and has to be estimated along with
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Separable Quaternion Matrix Factorization for Polarization Images SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-07-26 Junjun Pan, Michael K. Ng
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1281-1307, September 2023. Abstract. A transverse wave is a wave in which the particles are displaced perpendicular to the direction of the wave’s advance. Examples of transverse waves include ripples on the surface of water and light waves. Polarization is one of the primary properties of transverse waves. Analysis of polarization states can
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A Class of Priors for Color Image Restoration Parameterized by Lie Groups Acting on Pixel Values SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-07-25 Thomas Batard
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1235-1280, September 2023. Abstract. In a recent paper [T. Batard, G. Haro, and C. Ballester, SIAM J. Imag. Sci., 14 (2021), pp. 1816–1847], a new prior for image restoration was introduced. It relies first on the observation that an image and a degraded version of it can share some visual content and then on the conjecture that an image restoration
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Theoretical Foundation of the Stretch Energy Minimization for Area-Preserving Simplicial Mappings SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-07-21 Mei-Heng Yueh
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1142-1176, September 2023. Abstract. The stretch energy is a fully nonlinear energy functional that has been applied to the numerical computation of area-preserving mappings. However, this approach lacks theoretical support and the analysis is complicated due to the full nonlinearity of the functional. In this paper, we establish a theoretical
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Efficient Bayesian Computation for Low-Photon Imaging Problems SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-07-24 Savvas Melidonis, Paul Dobson, Yoann Altmann, Marcelo Pereyra, Konstantinos Zygalakis
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1197-1236, September 2023. Abstract. This paper studies a new and highly efficient Markov chain Monte Carlo (MCMC) methodology to perform Bayesian inference in low-photon imaging problems, with particular attention given to situations involving observation noise processes that deviate significantly from Gaussian noise, such as binomial, geometric
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Spherical Image Inpainting with Frame Transformation and Data-Driven Prior Deep Networks SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-07-24 Jianfei Li, Chaoyan Huang, Raymond Chan, Han Feng, Michael K. Ng, Tieyong Zeng
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1179-1196, September 2023. Abstract. Spherical image processing has been widely applied in many important fields, such as omnidirectional vision for autonomous cars, global climate modeling, and medical imaging. It is nontrivial to extend an algorithm developed for flat images to the spherical ones. In this work, we focus on the challenging
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Provable Phase Retrieval with Mirror Descent SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-07-14 Jean-Jacques Godeme, Jalal Fadili, Xavier Buet, Myriam Zerrad, Michel Lequime, Claude Amra
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1106-1141, September 2023. Abstract. In this paper, we consider the problem of phase retrieval, which consists of recovering an [math]‐dimensional real vector from the magnitude of its [math] linear measurements. We propose a mirror descent (or Bregman gradient descent) algorithm based on a wisely chosen Bregman divergence, hence allowing us
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Matrix Balancing Based Interior Point Methods for Point Set Matching Problems SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-07-13 Janith Wijesinghe, Pengwen Chen
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1068-1105, September 2023. Abstract. Point set matching problems can be handled by optimal transport. The mechanism behind it is that optimal transport recovers the point-to-point correspondence associated with the least curl deformation. Optimal transport is a special form of linear programming with dense constraints. Linear programming can
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WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-07-12 Fabian Altekrüger, Johannes Hertrich
SIAM Journal on Imaging Sciences, Volume 16, Issue 3, Page 1033-1067, September 2023. Abstract. Exploiting image patches instead of whole images has proved to be a powerful approach to tackling various problems in image processing. Recently, Wasserstein patch priors (WPPs), which are based on the comparison of the patch distributions of the unknown image and a reference image, were successfully used
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On Assignment Problems Related to Gromov–Wasserstein Distances on the Real Line SIAM J. Imaging Sci. (IF 2.1) Pub Date : 2023-06-23 Robert Beinert, Cosmas Heiss, Gabriele Steidl
SIAM Journal on Imaging Sciences, Volume 16, Issue 2, Page 1028-1032, June 2023. Abstract. Let [math] and [math], [math], be real numbers. We show by an example that the assignment problem \begin{align*} \max_{\sigma \in S_n} F_\sigma (x,y) := \frac 12 \sum_{i,k=1}^n |x_i- x_k|^\alpha \, |y_{\sigma (i)}- y_{\sigma (k)}|^\alpha, \quad \alpha \gt 0, \end{align*} is in general neither solved by the identical