An introduction to compressive sensing for digital signal reconstruction and its implementation on digital image reconstruction

Abstract

Shannon/Nyquist theorem underlies most of the algorithms in signal processing and data acquisition in such a way that the required sampling rate is at least 2 times the frequency of the signal. However there are many cases in which most of the information covers at some particular components while the rest is worthless. Therefore it is very useful if those significant components can be directly collected instead of wasting bandwidth for the unnecessary ones. Compressive Sensing (CS) is an algorithm that minimizes the sampling rate of the signals while still retaining the necessary information for the reconstruction process. It bypasses the current algorithms in which large amount of data is collected and then remove in a consequent compression step. Every CS algorithms are the combination of random kernels and non parametric estimation techniques. In general, the reconstruction framework estimates an under determined linear system of solutions with an unknown compressible or sparse signals. CS is applied broadly and be a novel algorithm in signal processing including: Channel Coding, Inverse Problem, Data Compression, Data Acquisition and in some fields where hardware has limitation.