Research On Compressed Sensing Reconstruction Algorithm

Compressed sensing(CS)theory breaks through the limitation of the traditional Shannon Sampling theorem.,the signal processing method under the framework of compressed sensing theory greatly reduces the cost of signal sampling and recovery by directly perceiving the key information of the signal.The theory has enriched the signal sampling theory to a large extent and broadened the horizon of research in related fields,which has great research value and application prospect.The core content of CS theory includes the design of sparse transformation matrix of signal,the construction of signal measurement matrix and compressive sensing reconstruction algorithm.Among them,the high efficiency and stability reconstruction algorithm is the joint link which brings the CS theory into practice.Therefore,the research on the CS reconstruction algorithm has a bright application prospect and great scientific research value.The research of this paper is based on this,and the following shows the core content of my research and innovation work:(1)In this paper,the existing common CS reconstruction algorithm has been combed,the greedy reconstruction algorithms were deeply studied,through a large number of simulation experiments,the computational complexity and reconstruction probability of those algorithm have been analyzed.(2)In the process of atom selection,a stochastic strategy matching pursuit algorithm(RSMP)is proposed by abandoning the deterministic atomic selection mode and introducing appropriate randomness in the process of atom selection.Compared to the Multipath Matching Pursuit(MMP),the algorithm is not only simpler in mathematics and convenient in programming,but also the RSMP algorithm achieves the purpose of expanding the search range by using the single-path random search method.RSMP algorithm is flexible and can select the right number of atoms in each iteration.Compared with the gOMP algorithm,RSMP algorithm has less input parameters,stronger noise robustness and better reconstruction performance.(3)Further research on the appropriate random atom selection strategy in RSMP algorithm,combined with the ‘preferred' idea of the selection operator in the genetic algorithm,proposed a variety of random atom selection strategies,and detailed the atomic selection steps.A large number of simulation experiments show that these random atom selection strategies are more powerful than traditional deterministic atomic selection strategies for correct atom support set.To some extent,this random atomic selection enriches the way of atomic expansion of greedy algorithms and provides a new way for the atomic selection strategy of greedy algorithms.