Polynomial Preconditioners for Regularized Linear Inverse Problems

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-01-22 DOI:10.1137/22m1530355

Siddharth S. Iyer, Frank Ong, Xiaozhi Cao, Congyu Liao, Luca Daniel, Jonathan I. Tamir, Kawin Setsompop

引用次数: 0

Abstract

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 assume any explicit structure on the linear function and thus can be deployed in diverse applications of interest. The efficacy of the preconditioner is validated on three different Magnetic Resonance Imaging applications, where it is seen to achieve faster iterative convergence (around [math] faster, depending on the application of interest) while achieving similar reconstruction quality.

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正则化线性逆问题的多项式预调器

SIAM 影像科学杂志》，第 17 卷第 1 期，第 116-146 页，2024 年 3 月。摘要本研究旨在加速用于解决正则化线性逆问题的近似梯度法的收敛速度。这是通过设计一种基于多项式的预处理器来实现的，该预处理器以线性算子导出的正则算子的特征值谱为目标。该预处理器不假定线性函数有任何显式结构，因此可用于各种相关应用。我们在三种不同的磁共振成像应用中验证了该预调器的功效，发现它能实现更快的迭代收敛（根据感兴趣的应用，大约快[数学]），同时获得相似的重建质量。

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

SIAM Journal on Imaging Sciences COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE-COMPUTER SCIENCE, SOFTWARE ENGINEERING

CiteScore

3.80

自引率

4.80%

发文量

审稿时长

>12 weeks

期刊介绍： SIAM Journal on Imaging Sciences (SIIMS) covers all areas of imaging sciences, broadly interpreted. It includes image formation, image processing, image analysis, image interpretation and understanding, imaging-related machine learning, and inverse problems in imaging; leading to applications to diverse areas in science, medicine, engineering, and other fields. The journal’s scope is meant to be broad enough to include areas now organized under the terms image processing, image analysis, computer graphics, computer vision, visual machine learning, and visualization. Formal approaches, at the level of mathematics and/or computations, as well as state-of-the-art practical results, are expected from manuscripts published in SIIMS. SIIMS is mathematically and computationally based, and offers a unique forum to highlight the commonality of methodology, models, and algorithms among diverse application areas of imaging sciences. SIIMS provides a broad authoritative source for fundamental results in imaging sciences, with a unique combination of mathematics and applications. SIIMS covers a broad range of areas, including but not limited to image formation, image processing, image analysis, computer graphics, computer vision, visualization, image understanding, pattern analysis, machine intelligence, remote sensing, geoscience, signal processing, medical and biomedical imaging, and seismic imaging. The fundamental mathematical theories addressing imaging problems covered by SIIMS include, but are not limited to, harmonic analysis, partial differential equations, differential geometry, numerical analysis, information theory, learning, optimization, statistics, and probability. Research papers that innovate both in the fundamentals and in the applications are especially welcome. SIIMS focuses on conceptually new ideas, methods, and fundamentals as applied to all aspects of imaging sciences.