Non-coherent Approximation And Reconstruction Error Based Compressed Sensing Observation Matrix Optimization

Compressed sensing theory is based on the sparseness or compressibility of the signal.It uses non-coherent linear observation projection to simultaneously sample and compress the signal,and uses a non-linear reconstruction algorithm to recover the high-dimensional original signal from the low-dimensional observations.This theory was widely used shortly after it was proposed,especially in the fields of image signal processing,medical imaging,wireless communication,radar imaging,information coding,pattern recognition,etc.The three components of the theory include: sparse representation of nature signals,design of the observation matrices,and efficient reconstruction algorithms.Among them,the design of the observation matrix is the key of the compressed sensing theory,and the effective observation matrix is the guarantee for the high probability and accurate reconstruction of the original signal.Based on the constraints of observation matrices,this thesis conducts in-depth research on the optimization algorithms of observation matrices from two aspects that reducing the coherence of perception matrices and improving the robustness of observation matrices.The innovative results obtained are as follows:1.In order to reduce the coherence between the observation matrix and the sparse matrix to approximate the coherence Welch boundary,in this thesis,an optimization algorithm of observation matrix based on a non-coherent approximation method is proposed.Firstly,constructing a non-coherent unit norm tight framework,the observation matrix is initialized as a random partial Fourier matrix,and making the sensing matrix directly approximate to the unit norm tight framework.The constructed tight framework avoids the difficulty of constructing equiangular tight frames.The experimental results show that compared with the existing framework-based optimization algorithms,the proposed algorithm effectively reduces the average mutual coherence of the sensing matrix and improves the reconstruction accuracy of the image signal.2.In order to improve the robustness of the image compressed sensing system,to improve the anti-noise performance,in this thesis,an observation matrix optimization algorithm based on image reconstruction errors is proposed.Based on the traditional Gram matrix based optimization model,the reconstruction error information of the image signal is added as a regular term to the traditional model,and the Frobenius norm expansion and singular value decomposition of the matrix are used to reduce the computational complexity of the algorithm,which ensures effective convergence of the algorithm.Finally,a gradient descent algorithm is used to solve the observation matrix.Experimental results show that compared with the state-of-the-art observation matrix optimization algorithm,the proposed algorithm significantly improves the robustness of the image compressed sensing system,effectively reduces the average coherence coefficient,and the peak signal-to-noise ratio of the image can be increased by up to 1.3dB.