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.