Signal Reconstruction via Compressive Sensing

Compressive sensing is a new approach of sampling theory, which assumes that signal can be exactly recovered from incomplete information. It relies on properties such as incoherence, signal sparsity and compressibility, and does not follow traditional acquisition process based on transform coding. Sensing procedure is very simple, nonadaptive method that employs linear projections of signal onto test functions. Set of test functions is arranged in the measurement matrix that allows acquiring random samples of original signal. Signal reconstruction is achieved from small amount of data by an optimization process which has the aim to find the sparsest vector with transform coefficients among all possible solutions. This paper gives an overview of compressive sensing theory, background, measurement and reconstruction processes. Reconstruction process was presented on a few types of signals at the end of this paper. Experimental results show that accurate reconstruction is possible for various type of signals.