A sampling greedy average regularized Kaczmarz method for tensor recovery

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2024-05-07 DOI:10.1002/nla.2560

Xiaoqing Zhang, Xiaofeng Guo, Jianyu Pan

引用次数: 0

Abstract

Recently, a regularized Kaczmarz method has been proposed to solve tensor recovery problems. In this article, we propose a sampling greedy average regularized Kaczmarz method. This method can be viewed as a block or mini‐batch version of the regularized Kaczmarz method, which is based on averaging several regularized Kaczmarz steps with a constant or adaptive extrapolated step size. Also, it is equipped with a sampling greedy strategy to select the working tensor slices from the sensing tensor. We prove that our new method converges linearly in expectation and show that the sampling greedy strategy can exhibit an accelerated convergence rate compared to the random sampling strategy. Numerical experiments are carried out to show the feasibility and efficiency of our new method on various signal/image recovery problems, including sparse signal recovery, image inpainting, and image deconvolution.

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用于张量恢复的采样贪婪平均正则化卡兹马兹方法

最近，有人提出了一种正则化 Kaczmarz 方法来解决张量恢复问题。在本文中，我们提出了一种采样贪婪平均正则化 Kaczmarz 方法。这种方法可以看作是正则化 Kaczmarz 方法的分块或小批量版本，它是基于对若干正则化 Kaczmarz 步长进行平均，步长为恒定或自适应外推步长。此外，它还配备了从传感张量中选择工作张量切片的采样贪婪策略。我们证明了我们的新方法在期望值上是线性收敛的，并表明与随机抽样策略相比，贪婪抽样策略能表现出更快的收敛速度。通过数值实验，我们证明了新方法在各种信号/图像复原问题上的可行性和效率，包括稀疏信号恢复、图像内绘和图像解卷积。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.