Sparse Signal Reconstruction Based On Phase Retrieval Threshold Algorithm And Internal Projection Neural Network Algorithm

With the development of information technology and the advent of the era of big data,the demand for information is also increasing,which has brought new challenges for the signal sampling,data storage and transmission.Sparse signal recovery has received more and more attention and has been widely used in many fields such as signal processing,compressed sensing,machine learning,statistics and so on.In this paper,based on compressed sensing,special measurement matrices are selected to study the reconstruction of sparse signals.The main contents of this paper are as follows:The first chapter introduces the research background of compressed sensing and sparse signal recovery,the history and current status of research on compressed sensing and sparse signal reconstruction at home and abroad,summarizes the main work and organizational structure of this paper.In the second chapter,we introduce the theory of sparse signal reconstruction,which includes the following three core problems: sparse representation of signal,design of measurement matrix and signal reconstruction algorithm.In the third chapter,we introduce the phase retrieval problem of sparse signal,and study the sparse signal recovery in the case of lack of phase information,and propose a new iterative hard threshold(IHT)algorithm to solve the phase retrieval.Then,the idea of backtracking is added to the IHT algorithm,which is based on the backtracking iterative hard threshold algorithm(BIHT),which overcomes the disadvantage of IHT instability,and improves the speed and accuracy of computation.In the fourth chapter,the interior point projection neural network(IPNN)algorithm for sparse signal reconstruction is proposed.Firstly,a non convex minimization problem is proposed for sparse signal reconstruction from the measurement matrix with high coherence.We introduce the IPNN to solve the nonconvex minimization problem,and prove the convergence of IPNN under certain conditions.Finally,a series of experiments show the effectiveness of IPNN for the minimization method.The fifth chapter summarizes the work done in this paper,and makes an analysis and prospect of the contents of this paper.