A new sufficient condition for sparse vector recovery via ℓ1 − ℓ2 local minimization

IF 2 2区数学 Q1 MATHEMATICS

Analysis and Applications Pub Date : 2021-04-10 DOI:10.1142/S0219530521500068

Ning Bi, J. Tan, Wai-Shing Tang

引用次数: 2

Abstract

In this paper, we provide a necessary condition and a sufficient condition such that any [Formula: see text]-sparse vector [Formula: see text] can be recovered from [Formula: see text] via [Formula: see text] local minimization. Moreover, we further verify that the sufficient condition is naturally valid when the restricted isometry constant of the measurement matrix [Formula: see text] satisfies [Formula: see text]. Compared with the existing [Formula: see text] local recoverability condition [Formula: see text], this result shows that [Formula: see text] local recoverability contains more measurement matrices.

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给出了稀疏向量通过1 ~ 2局部极小化恢复的一个新的充分条件

在本文中，我们提供了一个必要条件和一个充分条件，使得任何[公式：见文本]-稀疏向量[公式：看文本]都可以通过[公式：见图文本]局部最小化从[公式：可见文本]中恢复。此外，我们进一步验证了当测量矩阵[公式：见正文]的受限等距常数满足[公式：看正文]时，充分条件自然有效。与现有的[公式：见正文]局部可恢复性条件[公式：见图正文]相比，该结果表明[公式：看正文]局部的可恢复性包含了更多的测量矩阵。

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

Analysis and Applications 数学-数学

CiteScore

3.90

自引率

4.50%

发文量

审稿时长

>12 weeks

期刊介绍： Analysis and Applications publishes high quality mathematical papers that treat those parts of analysis which have direct or potential applications to the physical and biological sciences and engineering. Some of the topics from analysis include approximation theory, asymptotic analysis, calculus of variations, integral equations, integral transforms, ordinary and partial differential equations, delay differential equations, and perturbation methods. The primary aim of the journal is to encourage the development of new techniques and results in applied analysis.