Research On Algorithm Of Sampling And Optimization Algorithm Of Measurement Matrix Of Compressed Sensing

The theory of compressed sensing broke the original Nyquist sampling theorem,it is put forward that Sampling and compressing can be carried out simultaneously.It can reconstruct the original signal with high probability when the signal sampling frequency in less than two times of the original signal.By using the sparsity of the signal,the theory reduces the cost of sampling and storage of the signal.Compressed sensing theory has attracted a lot of scholars" attention.In this paper,we mainly study the optimization of the observation matrix and the reconstruction algorithm of the compressed sensing,and the main work is as follows:Firstly,we have improved the sampling strategy in the image block compressed sensing theory.We divide the observed matrix into the smooth image block and the non smooth image block according to the energy of the observation vector.And we sampling the smooth blocks again.The experimental results show that the adaptive block sampling algorithm we proposed is more accurate than the traditional block sampling algorithm in the case of the same reconstruction algorithm.Then,we studied three kinds of observation matrix,and we are discussed the structure of the three kinds of observation matrix and the advantages and disadvantages of each kind of matrix respectively.In order to improve the performance of the observation matrix,we further study on the observation matrix optimization method based on Gram matrix structure.By analysizing respectively the Elad optimization method,the gradient descent optimization method,we find that these algorithms are achieve the optimization of observation the purpose of matrix by reducing the value of non diagonal elements of Gram matrix to decrease the coefficient between the sparse matrix and observation matrix.For the gradient descent method,it can only reduce the limitation of the non diagonal elements of the Gram matrix.We is improve the original algorithm by the method of eigenvalue decomposition,and we redefined the error function.The improved gradient descent optimization method ismore suitable for large scale problems.And we verifiy the effectiveness of the improved algorithm by experiments.Finally,Compressed-sensing sampling with smoothed projected landweber has the disadvantage of poor quality of reconstructed image with low sampling rate.Total variation can improve the reconstruction effect to a certain extent,but it can reduce the operation speed.we propose an adaptive sampling method based on multi scales.According to the weight of the wavelet decomposition of different layers on the results of influence of different adaptive assigned to each layer of different sampling rate,and the reconstruction will be applied when a smooth iterative threshold projection method to each sub block with each layer.The experimental results show that compared with the traditional iterative threshold projection method,the reconstruction quality is improved by1-3dB,and the reconstruction speed is equal to that of the iterative threshold projection method and is better than the total variation method.