Research On Compressed Sensing Signal Reconstruction Algorithm Based On Evolutionary Multi-Objective Optimization

Signal processing plays an important role in the development of science and technology,and sampling is an indispensable part of signal processing.In the background of big data,people are increasingly demanding technical requirements for signal processing.Based on the traditional Nyquist sampling theorem,the requirements for massive data processing techniques have not been met.Compressed sensing theory has broken through the limitations of Nyquist's theorem and got a rapid development,it provides a new way of thinking for the information processing field.This method does not sample the original signal at high speed,but directly samples the information in the signal to overcome the problem of ultra-wideband signals.During processing,the compressed sensing simultaneously performs sampling and compression,which greatly reduces the storage and transmission overhead of the terminal devices.Finally,a sery of optimization methods are used to accurately reconstruct the original signal with a small amount of acquisition information.The sparse representation of signals,the construction of observation matrices,and the design of reconstruction algorithms in compressed sensing theory have been the focus of research.Signal reconstruction is the final step to directly determine the success or failure of the compressed sensing system.Therefore,this paper mainly studies the reconstruction algorithm in order to propose a reconstruction algorithm with higher reconstruction precision and better performance.The main works include:?1?In this paper,the compressed sensing reconstruction algorithm is deeply studied,and the existing reconstruction methods are comprehensively sorted out through reading a lot of documents.In order to solve the reconstruction problem by using penalty function method,weight parameters need to be introduced to make the reconstruction effect change dramatically.Therefore,this paper mainly explores how to solve this problem.?2?For the penalty function method,a regularization parameter is usually used to aggregate the measurement error term and the sparse term into a single objective function.It is difficult to achieve the equilibrium optimization of the two targets.For this reason,this paper takes the measurement error and the sparse constraint as an optimization objective function respectively,by establishing a multi-objective model to avoid introducing weight parameters,then the heavy task of adjusting weight parameters is fundamentally solved.?3?In order to solve the above multi-objective problem,this paper proposes an adaptive local search evolution multi-objective algorithm,which designs two local search methods based on L₁ norm and L_1/2 norm to improve the quality of each solution and obtain the current optimal solution.On the one hand,in order to fully exploit the information of the two solutions to maintain the diversity,a competitive strategy is also designed to select the best solution of the current round to form adaptation method,so as to ensure the global optimal solution.On the other hand,to make full use of the information of the two solutions to maintain the diversity,a competition strategy is also designed to form an adaptative method to ensure the global optimal solution.?4?The feasibility of the proposed method is proved by experiments,and compare it with other nine algorithms in the signal reconstruction error,which highlights the advantages of the proposed algorithm.