The Null Space Property of the Weighted ℓr − ℓ1 Minimization

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING International Journal of Wavelets Multiresolution and Information Processing Pub Date : 2023-04-07 DOI:10.1142/s0219691323500212

Jianwen Huang, Xinling Liu, Jinping Jia

引用次数: 0

Abstract

. The null space property (NSP), which relies merely on the null space of the sensing matrix column space, has drawn numerous interests in sparse signal recovery. This article studies NSP of the weighted ℓ r − ℓ 1 minimization. Several versions of NSP of the weighted ℓ r − ℓ 1 minimization including the weighted ℓ r − ℓ 1 NSP, the weighted ℓ r − ℓ 1 stable NSP, the weighted ℓ r − ℓ 1 robust NSP, and the ℓ q weighted ℓ r − ℓ 1 NSP for 1 ≤ q ≤ 2, are proposed, as well as the associating considerable results are derived. Under these NSP, suﬃcient conditions for the recovery of (sparse) signals with the weighted ℓ r − ℓ 1 minimization are established. Furthermore, we show that to some extent, the weighted ℓ r − ℓ 1 stable NSP is weaker than the restricted isometric property (RIP). And the RIP condition we obtained is better than that of Zhou Z. (2022).

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加权的零空间性质ℓr−ℓ1最小化

零空间特性（NSP）仅依赖于感测矩阵列空间的零空间，在稀疏信号恢复中引起了许多兴趣。本文研究加权的NSPℓ r−ℓ 1最小化。加权的NSP的几个版本ℓ r−ℓ 1最小化，包括加权ℓ r−ℓ 1 NSP，加权ℓ r−ℓ 1个稳定的NSP，加权ℓ r−ℓ 1个强大的NSP，以及ℓ q加权ℓ r−ℓ 提出了1≤q≤2的1 NSP，并得到了相应的可观结果。在这些NSP下，恢复（稀疏）信号的充分条件ℓ r−ℓ 1最小化。此外，我们还表明，在某种程度上ℓ r−ℓ 1稳定的NSP比限制等距性质（RIP）弱。并且我们得到的RIP条件比周中的要好。（2022）。

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

International Journal of Wavelets Multiresolution and Information Processing 工程技术-计算机：软件工程

CiteScore

2.60

自引率

7.10%

发文量

审稿时长

2.7 months

期刊介绍： International Journal of Wavelets, Multiresolution and Information Processing (hereafter referred to as IJWMIP) is a bi-monthly publication for theoretical and applied papers on the current state-of-the-art results of wavelet analysis, multiresolution and information processing. Papers related to the IJWMIP theme are especially solicited, including theories, methodologies, algorithms and emerging applications. Topics of interest of the IJWMIP include, but are not limited to: 1. Wavelets: Wavelets and operator theory Frame and applications Time-frequency analysis and applications Sparse representation and approximation Sampling theory and compressive sensing Wavelet based algorithms and applications 2. Multiresolution: Multiresolution analysis Multiscale approximation Multiresolution image processing and signal processing Multiresolution representations Deep learning and neural networks Machine learning theory, algorithms and applications High dimensional data analysis 3. Information Processing: Data sciences Big data and applications Information theory Information systems and technology Information security Information learning and processing Artificial intelligence and pattern recognition Image/signal processing.

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