Improvement And Research Of Compressed Sensing Reconstruction Algorithms

In the traditional Nyquist sampling theory,the premise of obtaining original and complete information is that the sampling frequency is more than twice the signal bandwidth,which brings great pressure to hardware system,storage processing and cost.In recent years,the Compressed Sensing(CS)idea of Candes and Donoho has restored high-dimensional signals from low-dimensional data acquired by low-speed sampling,which is no longer limited to the requirement of sampling frequency,avoided generating a large number of redundant data and saved storage space,and brought about innovative progress in signal processing technology.The research of reconstruction algorithm is the most fundamental step to apply compressed sensing to the real world,and it is also the focus and difficulty of compressed sensing.This dissertation focuses on the reconstruction algorithm.Based on the classical compressed sensing algorithm,two improved algorithms are proposeds to overcome the shortcomings of existing algorithms.The main research of this dissertationincludes:1.An improved regularized smoothing l0 norm reconstruction algorithm(AReSLO)is proposed in this dissertation,which increases the robustness of the algorithm in the case of noise and reduces the error caused by bad conditions.According to the definition of approximate l0 norm reconstruction algorithm,this algorithm combines the advantages of fractional function used by ALO algorithm with the high robustness of ReSLO algorithm.Regularization parameters are added to consider the noise situation.Two minimization iteration formulas are used to solve the two pats of the mathematical model,which solves the problem of low robustness of ALO algorithm in noise condition.2.An improved variable step size optimal subspace tracking algorithm(VssOSP)is proposed in this dissertation,which solves the problem that the sparsity of the step-by-step optimal subspace algorithm(SOSP)is known.This problem limits the application scope of the algorithm.The idea of variable step size and the relationship curve between the number of support sets and residuals are used to improve the reconstruction accuracy and recovery performance of the algorithm.The algorithm is based on the theory of optimum amplification and reduction of atoms.Firstly,the initial fixed step size and initial support set are obtained by matching test formulas.Secondly,the increment and deletion iteration formulas are used to judge the atoms of support set in the process of adding or subtracting atoms,and the location interval of sparsity is determined by the signal residual decline curve.Finally,the golden section method is used to gradually divides interval and gets the sparsity.The sparsity and support set are obtained,and the original sparse signal is reconstructed finally.In short,the reconstruction algorithm in this dissertation has high restoration accuracy and good visual effect for one-dimensional signal and two-dimensional image in the simulation experiment.It has certain research significance in the field of image analysis and processing.