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.