Non-local BV functions and a denoising model with L 1 fidelity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-30 DOI:10.1515/acv-2023-0082

Konstantinos Bessas, Giorgio Stefani

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引用次数: 0

Abstract

We study a general total variation denoising model with weighted L 1

{L^{1}}

fidelity, where the regularizing term is a non-local variation induced by a suitable (non-integrable) kernel K, and the approximation term is given by the L 1

{L^{1}}

norm with respect to a non-singular measure with positively lower-bounded L ∞

{L^{\infty}}

density. We provide a detailed analysis of the space of non-local BV

\mathrm{BV}

functions with finite total K-variation, with special emphasis on compactness, Lusin-type estimates, Sobolev embeddings and isoperimetric and monotonicity properties of the K-variation and the associated K-perimeter. Finally, we deal with the theory of Cheeger sets in this non-local setting and we apply it to the study of the fidelity in our model.

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非局部 BV 函数和保真度为 L 1 的去噪模型

我们研究了一种具有加权 L 1 {L^{1}}保真度的一般总变异去噪模型，其中正则化项是由合适的（不可积分的）核 K 引起的非局部变异，而逼近项则由相对于具有正下限 L ∞ {L^{infty}} 密度的非邢性度量的 L 1 {L^{1}}规范给出。我们详细分析了具有有限总 K 变量的非局部 BV \mathrm{BV} 函数空间，特别强调了 K 变量和相关 K 周长的紧凑性、Lusin 型估计、Sobolev 嵌入和等周性与单调性。最后，我们将讨论这种非局部设置中的切格集理论，并将其应用于我们模型中保真度的研究。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.