Sparse Signal Recovery Algorithms Based On Tail Optimization

Compressed sensing（CS）is a new signal sampling and processing theory that has emerged in recent years.It uses the sparsity of the signal to reconstruct signals from measurements that are much lower than the traditional Nyquist sampling frequency.The theory of CS has greatly relieved the pressure of signal storage and transmission,and has become one of the important technologies in the field of signal processing.The sparse signal recovery（reconstruction）problem is one of the core problems of CS,and the difficulty lies in constructing an effective sparse signal recovery algorithm.Distributed compressed sensing（DCS）is based on the theory of CS,using the correlation of the structure within the signal and among the signals to perform joint reconstruction of multiple signals.Similarly,the joint sparse signal recovery problem is also one of the core issues in DCS.The main research content of this paper is the sparse signal recovery problem in CS and DCS.The specific research content is as follows:1.For the sparse signal recovery problem in CS,in order to solve the problem of slow signal recovery speed of the tail-₁ in the tail optimization algorithm,a sparse signal recovery algorithm based on tail optimization is proposed,which is called the tail Hadamard product parameterized algorithm（tail-HPP）.The relationship between tail-HPP and tail-₁ minimum solutions is analyzed.The proposed tail-HPP algorithm finds the solution of tail-₁ by the alternating ridge regression,which speeds up the signal recovery.The profile method,direct method,and multi-stage method are used to solve tail-HPP in this paper.2.For the joint sparse signal recovery problem in DCS,in this paper,the tail-₁ is extended to the decentralized joint signal reconstruction model,a distributed tail-₁minimization algorithm（D-tail-₁）is proposed.The necessary and sufficient condition for the unique solution of the D-tail-₁ is proved.Then,a distributed tail Hadamard product parameterized algorithm（DTail-HPP）is proposed to accelerate the D-tail-₁.A large number of numerical experiments show that DTail-HPP utilizes the correlation among signals structure and to support set information transmitted among network nodes,resulting in better signal reconstruction performance than the tail-HPP and other traditional joint sparse signal recovery algorithms.Figure[32]Table[2]Reference[87]...