Research On Compressed Sensing Reconstruction Algorithm Based On Projection Neural Network

Compressed Sensing(CS)theory is a new signal processing theory,which is also called compressed sampling or sparse sampling.In signal processing,compared with Nyquist Sampling Theorem,CS can restore the original signal with a smaller measure-ment value,thus reducing the cost of sampling signal and storage signal.In other words,if a signal is compressible or sparse in a transformation domain,the transformed high-dimensional signal can be projected onto a low-dimensional space through an observa-tion matrix unrelated to the transformation basis,and then the original signal can be re-constructed from these few projections with a high probability through optimization al-gorithm.In recent years,with the development of CS theory,researches in the field of sparse signal reconstruction have been widely applied.In this paper,the signal recon-struction problem in CS is studied,and two kinds of projection neural network algorithms are proposed to solve this problem:(1)A projection neural network algorithm with finite-time convergence to solve L₁-minimization problem is proposed for sparse signal reconstruction which based on pro-jection neural network(PNN).Compared with the existing PNN,the proposed projection neural network algorithm is combined with the sliding mode control technique.Under certain conditions,the stability of the proposed projection neural network algorithm in the sense of Lyapunov is analyzed and discussed,then the finite-time convergence of the proposed projection neural network algorithm is proved and the time upper bound is giv-en.Finally,simulation results on a numerical example and a contrast experiment show the effectiveness and superiority of our proposed projection neural network algorithm.(2)A new projection neural network algorithm for solving L₁-minimization prob-lem is proposed,which is based on classic projection neural network(PNN)and sliding mode control technique.Furthermore,the proposed projection neural network algorithm can be used to make sparse signal reconstruction and image reconstruction.Firstly,a sign function is introduced into the PNN model to design fixed-time projection neural network algorithm(FPNN).Then,under the condition that the projection matrix satisfies the Re-stricted Isometry Property(RIP),the stability and fixed-time convergence of the proposed FPNN are proved by Lyapunov method.Finally,based on the experimental results of sig-nal simulation and image reconstruction,the proposed FPNN shows the effectiveness and superiority compared with that of the existing projection neural network algorithms.