Researches On Adaptive Matching Pursuit Algorithms

Compressed sensing can sample and compress signals at the same time,this greatly reduces hardware pressure and signal processing costs.Compressed sensing provides a good solution to the growing challenge of massive data demands on storage space and transmission bandwidth,so compressed sensing become the best choice for signal processing.Reconstruction algorithm is a necessary method in the compressed sensing theory.There are two kinds of compressed sensing algorithms: greedy algorithms and convex optimization algorithms.The greedy algorithms are widely used because they are easy to implement and highly efficient.Based on several classical algorithms in the greedy algorithms,this thesis proposes improved algorithms.The main works are as follows:(1)Since the Stagewise Weak Orthogonal Matching Pursuit(SWOMP)will put the atoms which should not be selected into the support set during the iteration,in order to overcome this shortcoming,the Stagewise Weak Limited Orthogonal Matching Pursuit(SWLOMP)is proposed.The algorithm introduces a restricted rule and adaptively calculates the number of atoms which are added to the support set in each iteration,so that the poor performing atoms in each iteration can be removed from the support set.Simulation results show that the algorithm has good signal reconstruction quality for one-dimensional signal.(2)Since the Stage-wise Orthogonal Matching Pursuit(StOMP)will mistakenly select the atoms into the support set,resulting in poor signal reconstruction quality,in order to overcome this shortcoming,the Stage-wise Limited Orthogonal Matching Pursuit(StLOMP)is proposed.By adding a restricted rule on the original algorithm,adaptively calculates the number of atoms which are added to the support set in each iteration,extra selected atoms in the support set can be deleted.Simulation results show that the signal reconstruction for one-dimensional signal is high.(3)For the Sparsity Adaptive Matching Pursuit(SAMP)needs to set the step-size in advance,and the selection of step-size greatly affects the effect of signal reconstruction,in order to overcome this shortcoming,the Sparsity and Step Adaptive Limited Matching Pursuit(SSALMP)is proposed.The algorithm can calculate the step-size adaptively according to the basic information.Meanwhile,the threshold is set to control the step-size,avoiding the wrong atoms to be selected into the support set.Simulation results show that the accuracy of signal reconstruction for one-dimensional signal is high.(4)The Orthogonal Multi-Matching Pursuit(OMMP)needs to set the the number of atoms in advance,and the selection of the number of atoms greatly affects the effect of signal reconstruction,in order to overcome this shortcoming,the Adaptive Multi-Limited Orthogonal Matching Pursuit(AMLOMP)is proposed.The maximum number of atoms added to the support set in each iteration can be calculated adaptively according to the formula.Moreover,the de-noising criterion is set to remove the atoms conforming to the de-noising standard from the support set.The simulation results show that the signal reconstruction for one-dimensional signal is of high quality.