压缩感知中确定性测量矩阵构造算法综述

A Survey on Deterministic Measurement Matrix Construction Algorithms in Compressive Sensing

测量矩阵在压缩感知中起着关键性的作用,其性能会影响原始信号的压缩与重构.现有的测量矩阵多数为随机的,它们在实际应用中有存储量大、效率低等缺点,且在硬件上难以实现,故构造确定性测量矩阵对压缩感知理论的推广与应用具有重要的意义.本文回顾了国内外学者在确定性测量矩阵构造方面的研究,着重对目前已有的构造算法进行详细的介绍和分类,最后根据多种指标综合评述了各种算法的性能.

Measurement matrix, whose performance can affect the compression and reconstruction of original signal, plays a key role in compressive sensing. Most of the existing measurement matrices are random ones, which have shortcomings in practical application, such as large storage capacity, low efficiency and difficulty when implemented in the hardware. Therefore, it is of im- portant practical significance to construct detennimstic measurement matrix for the promotion and application of the compressive sensing theory. In this paper, the existing construction algorithms for deterministic measurement matrix are reviewed, introduced and classified in detail. Finally the oerfonnances of all algorithms are summarized in terms of common indicators.