Research On The Reconstruction Of Compressed Sensing Signal By Smooth Neural Network Algorithm

Compressed sensing?CS?is a new kind of signal processing and sampling theory.The theory of compressed sensing indicates that the signal is sparse in a certain transfor-mation,then the high dimensional signal can be transformed to a relatively low dimension by a matrix?non-correlation matrix?with certain conditions,then the original signal can be reconstructed by using the signal reconstruction algorithm.The proposed theory of compressed sensing can not only effectively solve the problem of the separation of sam-pling and compression in the Nyquist sampling theorem,but also effectively reduce the cost of signal sampling and save the cost of signal storage.At present,the compressive sensing theory has gets widespread attention in many fields and has been used in practical problems widely.This article investigates the problem of signal reconstruction,which is an important problem in compressed sensing.The main research work is as follows:?1?For the reconstruction of compressed sensing signals without noise sampling,we investigate a more general mixed norm model and a smoothing neural network optimal method for compress sensing problem,where the objective function includes nonsmooth,nonconvex,and non-Lipschitz quasi-norm L_p-norms?1?p>0?and nonsmooth L_q-norms?2?q>1?,and its feasible set is a closed convex subset of Rⁿ.Firstly,under the restricted isometry property?RIP?condition,the uniqueness and existence of solu-tion for the minimization model with a given sparsity are obtained through the theoretical analysis.With a mild condition,we get that the larger of the q,the more effective of the sparse recovery model under sensing matrix satisfies RIP conditions at fixed p.Second-ly,to solve the above optimization problem,a smooth inertia projection neural algorithm?SIPNN?and related circuit implementation methods are put forward,where A smooth inertia projection neural algorithm and related circuit implementation methods are put forward where the smooth approximation technique is used to deal with the nonsmooth terms of the model and the projection method is used for addressing the constraints of lin-ear equality.Under certain conditions,the stability of the algorithm is proved by theory.Finally,convergence behavior and successfully recover performance experiments and a comparison experiment confirm the effectiveness of the proposed SIPNN algorithm.?2?In this paper,a smooth neural network algorithm is proposed to solve the problem of reconfiguration of CS signal with sampling noise,where the objective function is non-smooth L₁-norm and inequality constrained function is the generalized L_p,?2?p?1?,which is used as the metric for the residual error.Using the smoothing approximate tech-nique,the non-Lipschitz continuous gradient of L_p-norm can be avoided efficiently and the difficulties of using differential inclusion method are overcome.The stability and optimality of the proposed SNN are proved under some appropriate assumptions.Final-ly,Simulation results of numerical reconstruction simulation experiment and comparison experiment with classical algorithm to substantiate the effectiveness of the smooth neural network?SNN?algorithm.