Non-Lipschitz Variational Models and their Iteratively Reweighted Least Squares Algorithms for Image Denoising on Surfaces

IF 2.1 3区数学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

SIAM Journal on Imaging Sciences Pub Date : 2024-06-20 DOI:10.1137/23m159439x

Yuan Liu, Chunlin Wu, Chao Zeng

引用次数: 0

Abstract

SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1255-1283, June 2024.
Abstract.Image processing on surfaces has gotten increasing interest in recent years, and denoising is a basic problem in image processing. In this paper, we extend non-Lipschitz variational methods for 2D image denoising, including TV[math], to image denoising on surfaces. We establish a lower bound for nonzero gradients of the recovered image, implying the advantage of the models in recovering piecewise constant images. A new iteratively reweighted least squares algorithm with the thresholding and support shrinking strategy is proposed. The global convergence of the algorithm is established under the assumption that the object function is a Kurdyka–Łojasiewicz function. Numerical examples are given to show good performance of the algorithm.

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用于曲面图像去噪的非 Lipschitz 变分模型及其迭代加权最小二乘法算法

SIAM 影像科学杂志》，第 17 卷第 2 期，第 1255-1283 页，2024 年 6 月。摘要.近年来，曲面图像处理越来越受到关注，而去噪是图像处理中的一个基本问题。本文将TV[math]等用于二维图像去噪的非Lipschitz变分方法扩展到曲面图像去噪。我们建立了恢复图像的非零梯度下限，这意味着模型在恢复片断常数图像方面具有优势。我们提出了一种采用阈值和支持缩小策略的新的迭代再加权最小二乘法算法。在假设对象函数是 Kurdyka-Łojasiewicz 函数的前提下，确定了算法的全局收敛性。给出的数值示例显示了该算法的良好性能。

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.