Advances and perspectives on compressed sensing theory
压缩感知基本理论:回顾与展望

In the past century,the Shannon sampling theorem has underlain nearly all the modern signal acquisition techniques.It claims that the sampling rate must be at least twice the maximum frequency present in the signal.One inherent disadvantage of the theorem,however,is the large number of data samples particularly in the case of special-purpose applications.The sampling data have to be compressed for efficient storage,transmission and processing.Recently,Candès reported a novel sampling theory called compressed sensing,also known as compressive sampling (CS).The theory asserts that one can recover signals and images from far fewer samples or measurements,not strictly speaking,as long as one adheres to two basic principles:sparsity and incoherence,or sparsity and restricted isometry property.The aim of this article is to survey the advances and perspectives of the CS theory,including the design of sparse dictionaries,the design of measurement matrices,the design of sparse reconstruction algorithms,and our proposal of several important problems to be studied.