Compressive Sensing Technology Based On Deep Learning

Compressive sensing(CS)is a novel sampling theory,which can effectively use the sparse characteristics of signals to save the cost of data acquisition,transmission and storage.Therefore,it can be used in wireless communication,signal acquisition and other fields.However,due to "a dismatch of sparse dictionary and signal" and "nonlinear reconstruction algorithm is not accurate",there is a problem of "error in reconstruction signal"in traditional compressive sensing.This paper aims to solve the above problem by taking advantage of the two characteristics of deep learning,which are "end-to-end learning"and "with the increase of network complexity,the network can approximate any function".The specific work and achievements are as follows:1.In order to analyze the influence of sparse base and reconstruction algorithm on signal error in traditional compressed sensing,this paper compares different sparse transform bases such as discrete cosine transform,discrete wavelet transform,discrete Fourier transform and identity matrix based on Ultra Wide Band(UWB)and handwritten digital image signal(MNIST).Also,the Mean Square Error(MSE)and Peak signal-to-noise Ratio(PSNR)of UWB and MNIST reconstructed signals are compared between the greedy reconstruction algorithm and the convex optimization algorithm.Simulation results show that the MSE of the identity matrix is lower than that of other common sparse transform bases at each sampling rate for sparse one-dimensional signals in time domain.For the image signals,the PSNR of the wavelet base at each sampling rate is higher than that of other sparse transform bases.At the same time,compared with the convex optimization algorithm,the greedy algorithm can reconstruct the signal with less error in a short time.2.For the analysis of the influence between the sparse transform bases and reconstruction signals shown in 1,this paper presents a Generative Network Compressive Sensing reconstruction algorithm(GN-CS).GN-CS uses generative adversarial networks to obtain an algorithm which has a smaller reconstruction MSE than traditional algorithms without designing a sparse transform base.In order to ensure that the reconstructed sig-nal is as similar as possible to the real signal,GN-CS redesigns the loss function of the network by combining the constraints in traditional compressive sensing.Compared with the traditional algorithm,the innovation of GN-CS is embodied in the use of generative network to generate signals automatically instead of directly reconstructing signals,so as to advoid the design of sparse conversion basis.At the same time,another innovation of GN-CS is that GN-CS is an inert learning algorithm.Compared with the existing compressive sensing technology based on deep learning,GN-CS does not need a large amount of data for pre-training,and the algorithm can only reconstruct the signal with the same probability distribution of the training signal.Simulation results show that the MSE of the reconstructed signals obtained by GN-CS is lower than that obtained by using the traditional sparse basis for UWB signals.For MNIST signal,the PSNR of reconstructed signals obtained by GN-CS is higher than that obtained by using traditional sparse basis.3.Aiming at the shortcomings of Orthogonal Matching Pursuit(OMP)in greedy reconstruction algorithm,this paper proposes a DCR-OMP algorithm,which can greatly reduce the effect of MSE.This algorithm is a novel compressed sensing reconstruction algorithm based on the OMP and the Depthwith Convolutional ResNet(DCR).DCR-OMP solves the problem that the index that OMP algorithm looks for in each iteration with the greatest correlation with the residual may not be sparse.DCR-OMP utilizes two networks,one for index search and one for decision.Different from OMP algorithm,which uses inner product to obtain the index with maximum correlation with residuals,the search network uses big data to pre-train and decide the index with maximum correlation with residuals.Secondly,in order to ensure that the index is on the sparse point,the second judgment network is used to judge.If it is not at the location of the sparse point,it is iterated again.Simulation results show that compared with traditional OMP,the MSE of UWB signals reconstructed by DCR-OMP is smaller and the PSNR of MNIST signals reconstructed by DCR-OMP is higher.Moreover,under different Signal To Noise ratios(SNR),DCR-OMP has a stronger robustness.