Research On Reconstruction Algorithms Of Compressive Sensing

Compressive sensing (CS) is a rising fancy signal processing theory in recent years,which is different from Nyquist sampling theory. Nyquist sampling theorem pointed out:the sampling rate must be more than twice the highest frequency signal in order toreconstruct the original signal completely. Compressive sensing theory pointed out: we canuse small amount of signal values to reconstruct signal accurately, but the signal is sparse orcompressible. CS samples the signal in the same time while it is compressing, thus, the dataacquisition rate is significantly below Nyquist rate, and saves plenty of storage, computingand transmission resources, and has a broad application foreground.CS theory consists of three main areas: sparse presentation matrix, measurementmatrix and reconstruction algorithm. Reconstruction algorithm is one of the core content inCS, it determines whether the signal be recovered or not directly. Reconstruction algorithmsmainly include two aspects: algorithm complexity and reconstruction precision. Thealgorithm complexity limits the application of CS, and the algorithm precision shows thevalidity and performance. This paper combines the CS articles at home and abroad, andanalyses Basis Pursuit and matching pursuit (MP) algorithm greed algorithms, does a deepresearch and simulation on Orthogonal matching pursuit (OMP)、Stagewise OMP、Regularization OMP、Compressive Sampling Matching Pursuit、and Subspace Pursuit.This paper focuses on the Sparsity Adaptive matching pursuit (SAMP). It can adjuststep to reconstruct signals accurately while the sparsity of signal is unknown. SAMPcombines the signal support and back idea, and we use SAMP to reconstruct one-dimensionsignals and two-dimension images. From the simulation results, compared with the otheralgorithms, the total quality of SAMP is very considerable.