Sparse Signal Reconstruction Based On Tail Minimization

The emergence of compressed sensing has broken the limitations of traditional sampling theory,making signal transmission,storage,and processing more efficient and practical.This has led to a significant revolution in the field of signal processing.Within compressed sensing theory,the reconstruction algorithm plays a vital role in connecting with practical applications.Its efficiency and sparse signal recovery ability directly affect the algorithm’s performance and practical application effects.As we all know,as the signal sparsity increases,the difficulty of signal recovery also increases.The tail-l1 minimization algorithm is proposed for its excellent sparse signal recovery ability.In this paper,we study the l1 minimization problem and the lq(1≤q≤2)minimization problem based on this algorithm.The main work and research results are as follows:The fast iterative shrinkage-thresholding algorithm(FISTA)has received significant attention due to its simple iterative framework and high computational efficiency for solving the l1 minimization problem.Inspired by FISTA,the tail fast iterative threshold shrinkage algorithm(tail-FISTA)is proposed,which incorporates both the profile least squares and direct methods to derive its implementation.Furthermore,the convergence analysis for the algorithm for a fixed support set T is provided.Simulation results demonstrate that the tail-FISTA not only preserves the efficiency of FISTA but also greatly improves the ability to recover sparse signals.Sergey Voronin and Ingrid Daubechies propose iterative reweighted least squares(IRLS)algorithm for solving lq(1≤q ≤2)minimization problem.However,when q>1,the lq minimization problem no longer has sparsity.Therefore,based on the fact that tail optimization algorithm has better sparsity properties,tail iteratively reweighted least squares algorithm(tail-IRLS)is proposed and derives its basic iterative framework in this paper.Simulation results demonstrate that the tail-IRLS algorithm can successfully obtain sparse solutions and has better sparse signal recovery capabilities compared to other advanced sparse recovery algorithms.Figure[14]Table[2]Reference[89]...