以最优行数和略少的随机性满足限制等距性质

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2024-12-18 DOI:10.1016/j.ipl.2024.106553

Shravas Rao

引用次数: 0

摘要

对于所有k-稀疏向量x，如果‖Φx‖22近似等于‖x‖22，则矩阵Φ∈RQ×N满足受限等距性质。我们使用O(klog （N/k)) log (k)）位的随机性给出了具有最优Q=O（klog (N/k)）行的RIP矩阵的构造。主要的技术成分是将汉森-赖特不等式推广到ε偏分布。

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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Satisfying the restricted isometry property with the optimal number of rows and slightly less randomness

A matrix

Φ \in R^{Q \times N}

satisfies the restricted isometry property if

{‖ Φ x ‖}_{2}^{2}

is approximately equal to

{‖ x ‖}_{2}^{2}

for all k-sparse vectors x. We give a construction of RIP matrices with the optimal

Q = O (k \log (N / k))

rows using

O (k \log (N / k) \log (k))

bits of randomness. The main technical ingredient is an extension of the Hanson-Wright inequality to ε-biased distributions.

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来源期刊

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.