An Inexact Majorized Proximal Alternating Direction Method of Multipliers for Diffusion Tensors

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-08-19 DOI:10.1137/23m1607015

Hong Zhu, Michael K. Ng

引用次数: 0

Abstract

SIAM Journal on Imaging Sciences, Volume 17, Issue 3, Page 1795-1819, September 2024.
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.

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扩散张量的非精确大数近端交替方向乘法

SIAM 影像科学期刊》，第 17 卷第 3 期，第 1795-1819 页，2024 年 9 月。摘要：本文重点研究了从噪声观测中估计正半有限四阶张量场的去噪问题。通过将张量映射为矩阵秩小于或等于 3 的 6×6 对称正半有限矩阵，张量的正半有限性得以保留。对于去噪，我们建议使用张量场上的各向异性离散总变异函数作为正则化项。对于这种非凸、非光滑的优化问题，我们提出了一种不精确的近似交替方向乘法。我们证明，不超过 [math] 次迭代就能找到优化问题的 [math] 固定解。我们使用多纤维扩散加权成像数据测试了所提模型和算法的有效性，数值结果表明我们的方法在去噪性能方面优于现有方法。

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.