Development and Prospect of Compressive Sensing

Compressive Sensing(CS) is a new developed theoretical framework for information acquisition and processing,which is based on matrix analysis,statistical probability theory,topological geometry,optimization and opsearch,functional analysis and so on.The high-dimensional signals can be recovered from the low-dimensional and sub-Nyquist sampling data based on the compressibility of signals.It not only inspires us to survey the linear problem again,but also enriches the optimization approaches for signal recovery to promote the combination of mathematics with engineering application.Nowadays the researches on compressive sensing have developed from the earlier concept understanding,numerical simulation,principle verification,and primary system designation,to the deeper researches on theory,development and application of practical system.In this paper,we introduce the basic idea of compressive sensing,and the development history,current and future challenges.