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In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Numerical Analysis · Mathematics 2021-01-15 Barbara Kaltenbacher , Kha Van Huynh

Multi-energy CT based on compression sensing theory with sparse-view sampling can effectively reduce radiation dose and maintain the quality of the reconstructed image. However,when the projection data are noisy, the reconstructed image can…

Medical Physics · Physics 2019-12-04 Cheng Kai , Jiang Min , Jianqiao Yu , Sun Yi

Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the…

Numerical Analysis · Mathematics 2025-02-07 Ratikanta Behera , Saroja Kumar Panda , Jajati Keshari Sahoo

Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have…

Optimization and Control · Mathematics 2021-02-16 Xuemei Chen , Jing Qin

In order to determine the 3D structure of a thick sample, researchers have recently combined ptychography (for high resolution) and tomography (for 3D imaging) in a single experiment. 2-step methods are usually adopted for reconstruction,…

Image and Video Processing · Electrical Eng. & Systems 2020-07-21 Huibin Chang , Pablo Enfedaque , Stefano Marchesini

Radio-frequency (RF) tomographic imaging is a promising technique for inferring multi-dimensional physical space by processing RF signals traversed across a region of interest. However, conventional RF tomography schemes are generally based…

Information Theory · Computer Science 2017-12-19 Tao Deng , Xiao-Yang Liu , Feng Qian , Anwar Walid

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…

Methodology · Statistics 2023-09-28 Di Wang , Yao Zheng , Guodong Li

Tensor low-rank representation (TLRR) has demonstrated significant success in image clustering. However, most existing methods rely on fixed transformations and suffer from poor robustness to noise. In this paper, we propose a novel…

Computer Vision and Pattern Recognition · Computer Science 2025-10-24 Hui Chen , Xinjie Wang , Xianchao Xiu , Wanquan Liu

Atomic norm minimization is a convex optimization framework to recover point sources from a subset of their low-pass observations, or equivalently the underlying frequencies of a spectrally-sparse signal. When the amplitudes of the sources…

Information Theory · Computer Science 2021-02-24 Maxime Ferreira Da Costa , Yuejie Chi

Precise reconstruction of unknown quantum states from measurement data, a process commonly called quantum state tomography, is a crucial component in the development of quantum information processing technologies. Many different tomography…

Quantum Physics · Physics 2022-10-28 Ingrid Strandberg

In this paper, we utilize stochastic optimization to reduce the space complexity of convex composite optimization with a nuclear norm regularizer, where the variable is a matrix of size $m \times n$. By constructing a low-rank estimate of…

Machine Learning · Computer Science 2015-12-08 Lijun Zhang , Tianbao Yang , Rong Jin , Zhi-Hua Zhou

Computed tomography (CT) involves a patient's exposure to ionizing radiation. To reduce the radiation dose, we can either lower the X-ray photon count or down-sample projection views. However, either of the ways often compromises image…

Image and Video Processing · Electrical Eng. & Systems 2023-10-12 Wenjun Xia , Yongyi Shi , Chuang Niu , Wenxiang Cong , Ge Wang

Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…

Optimization and Control · Mathematics 2018-11-12 Christian Grussler , Pontus Giselsson

Matrix completion focuses on recovering a matrix from a small subset of its observed elements, and has already gained cumulative attention in computer vision. Many previous approaches formulate this issue as a low-rank matrix approximation…

Computer Vision and Pattern Recognition · Computer Science 2019-01-08 Shengke Xue , Wenyuan Qiu , Fan Liu , Xinyu Jin

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

Numerical Analysis · Computer Science 2018-05-23 Longhao Yuan , Chao Li , Danilo Mandic , Jianting Cao , Qibin Zhao

The cone of positive-semidefinite (PSD) matrices is fundamental in convex optimization, and we extend this notion to tensors, defining PSD tensors, which correspond to separable quantum states. We study the convex optimization problem over…

Optimization and Control · Mathematics 2025-11-10 Liding Xu , Ye-Chao Liu , Sebastian Pokutta

This paper proposes a precise signal recovery method with multilayered non-convex regularization, enhancing sparsity/low-rankness for high-dimensional signals including images and videos. In optimization-based signal recovery, multilayered…

Signal Processing · Electrical Eng. & Systems 2024-09-24 Akari Katsuma , Seisuke Kyochi , Shunsuke Ono , Ivan Selesnick

Much research has been devoted to the problem of restoring Poissonian images, namely for medical and astronomical applications. However, the restoration of these images using state-of-the-art regularizers (such as those based on multiscale…

Optimization and Control · Mathematics 2012-10-10 Mário A. T. Figueiredo , José M. Bioucas-Dias

Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…

Computer Vision and Pattern Recognition · Computer Science 2015-03-18 Dai-Qiang Chen , Li-Zhi Cheng

Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…

Analysis of PDEs · Mathematics 2022-01-26 Kim Knudsen , Aksel K. Rasmussen