| Nowadays,signal sampling has been guided by Shannon-Nyquist sampling theorem,the bandwidth determines the sampling rate.If the sampling rate is higher and higher,such as radar signal,MRI image and hyperspectral image classification.In 2006,a new sampling theory,Compressed Sensing(CS),emerged as the times require.The compression sensing theory breaks through the Shannon-Nyquist theorem that the sampling frequency is not less than twice the bandwidth of the signal.Only when the sampling frequency is not less than twice the bandwidth of the signal can the original signal be recovered with high probability from the sampled data,that is,it performs sampling and data compression simultaneously in the process of signal sampling and combines the two into one.This paper mainly focuses on the research of reconstruction algorithm in CS.The research of reconstruction algorithm is not only the most important step towards practical application,but also the most concerned part in compressed sensing theory.In this paper,the latest recovery algorithm is studied in depth,focusing on the performance of the algorithm in terms of objective function model,efficiency,reconstruction accuracy and reconstruction probability.An improved signal recovery algorithm model is proposed,and mathematical formula derivation and simulation experiments are carried out to verify it.Through the comparison and analysis with the latest algorithm,it can be seen that improved model significantly improves the recovery accuracy and robustness in the gaussian white noise environment.At the same time,the image restoration problem using the Quasi-norm model under impulse environment is studied,and the LpLq-ADMM algorithm is proposed.In this paper,the convex relaxation algorithm in recovery algorithms is studied in detail,and the key problems involved and the solutions are described in detail:1.The different cost function models,the selection of parameters,the analysis of convergence and the simulation of their recovery performance in convex relaxation algorithms are introduced in detail.In order to solve the problems of high computational complexity,poor recovery performance and robustness in the existing algorithms.this paper proposes an improved algorithm without losing the recovery accuracy of the signal2.The implementation of SL0 algorithm using Gaussian function instead of L0 norm and SL0 algorithm is mainly described.In chapter 3,the compound trigonometric function isproposed to replace L0 norm.Because the its graph is steeper than Gaussian function graph,its can better approximate the performance of L0 norm.In SL0 algorithm,the steepest descent method is used to solve the solution.Because the search path of the steepest descent method will appear jagged,the accuracy of the solution of the algorithm is not high.Aiming at the shortcomings of SL0 algorithm,Composite Trigonometric function Null-space Re-weighted Approximate L0 norm(CTNRAL0)is proposed to solve the problem of accuracy and convergence.Simulation results show that the accuracy of CTNRAL0 algorithm in the white noise environment is significantly higher than the existing convex relaxation algorithm.3.In chapter 4,LpLq-ADMM algorithm(p ?(7)0,2(8),q ?(7)0,1(8))based on alternating direction method of multipliers is proposed in the S?S noise(one kind of non-gaussian white noise).The probability density function distribution model of S?S noise is briefly analyzed,and the LpLq-ADMM objective function model,parameter selection and convergence proof are analyzed.The p and q values selected by simulation experiments make the reconstruction accuracy and robustness of sparse signals under S?S noise reach the optimal value,and the reconstruction probability of sparse signals is obtained under the optimal p and q values.Meanwhile,LpLq-ADMM algorithm is also applied to the restoration of medical images.Simulation results show that this algorithm has a good ability to suppress S?S noise,and its output Peak Signal to Noise Ration(PSNR)is higher than other comparison algorithms. |
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