Research On Theory And Application Of Sparse Signal Reconstruction Based On Neural Network Algorithms

We are in the midst of a digital revolution,and the latest developments in science and technology have led to the transformation of data processing.In order to meet the needs of the big data era,compressed sensing has been deeply studied in many important and emerging applications,such as image processing,information theory,medical imaging and so on.Based on the neural network model,the sparse signal recovery in compressed sensing is realized via reweighted l_1-2and l_1-?2minimization.The effectiveness of the proposed method is fully demonstrated theoretically and experimentally.The main contents are as follows:In the first chapter,the research background and current situation of compressed sensing are briefly introduced,followed by the main structure layout of this paper.In the second chapter,we first summarize the relevant knowledge of compressed sensing,then introduce the basic idea of using neural network model to solve optimization problems,emphatically describe how to improve the neural network model step by step to achieve better results,and introduce the advantages of inertial projection neural network compared with other models to solve optimization problems in compressed sensing.In the third chapter,an iterative inertial projection neural network?IPNNs?is proposed for sparse signal reconstruction.Unlike the conventional l₁minimizations with the use of standard convex relaxation,a more general nonconvex weighted l_1-2minimization problem is introduced to achieve sparse signal reconstruction under highly coherent measurement ma-trix.Convergence and stability of the algorithm are proved under certain conditions.In addition,numerical experiments are conducted to support the proposed IPNNs'remarkable performance in reweighted l_1-2minimization.Mathematical theory and experimental analysis have confirmed its ability in sparse signal recovery.In the fourth chapter,we extend the form of l_1-2to l_1-?2measure,and also use the neural network model to solve the non-convex l_1-?2minimization problem of sparse signal reconstruction.Through simulation experiments,we find the appropriate?and then compare several classical algorithms to highlight the advantages of IPNNl_1-?2algorithm in sparse signal reconstruction.The fifth chapter summarizes the full text and makes an analysis and prospect of the content that this paper can continue to study.