Research Of Signal Reconstruction Algorithms Based On Compressed Sensing

Compressed Sensing(CS) is a new efficient signal sampling theory.For sparse or compressiblesignal,the data compression can be executed during signal sampling,so that a large amount of unlessdata can be avoided.Compressed sensing theory has broken the traditiona l Nyquist samplingtheorem.Firstly,this paper introduced the main theory of compressed sensing:the sparse representation,the design of measurement matrix and the reconstruction algorithms.The sparse representation withdifferent basis and matching pursuit algorithms will be mainly studied.Then we analysis the OMP,ROMP,SP,CoSaMp,SAMP by simulating.Secondly,considered that the sparse representation is depend on the sparse basis,and a singlesparse base may not be suited to all the signals,thus presents a new methord named compressedsensing reconstruction algorithms based on EMD.This algorithm using the EMD to decompose thesignal into a finite number of Intrinsic Mode Function components and a residue,then according tothe different frequency characteristics of the components, find better sparse basis, so that thesecomponents can have better sparse representation and archives the goal of using less number ofmeasurements to reconstruct the original signal and reconstruction performance is better.Finally,the traditional algorithms didn’t take into account the internal structure of the signal.Thus for block-sparse signals with special feture,an orthogonal multimatching pursuit algorithm(BOMMP) for block-sparse signals recovery has been proposed in this paper.A sufficient conditionfor the proposed algoritnm is given and proved,which shows it’s universally applicable. BOMMPhas two characteristics:high recovery probability because of considering of the internal structure ofthe signal;low computational complexity because of the multimatching idea.The simulation resultsdemonstrate that BOMMP has these features:high recovery probability, low computationalcomplexity and short runtime.Then combine the EMD with BOMMP,propose a new algorithmnamed BOMMP based EMD. The simulation results demonstrate that this algorithm has highrecovery probability and short runtime.