Research On Measurement Matrix Optimization And Algorithm Of Signal Reconstruction Of Compressed Sensing

Compressed sensing(CS), which breaks the limitations of the traditional Nyquist sampling theorem, takes full advantage of the sparse signal sparse characteristics to achieve the accurate reconstruction of signal under low sampling rate,which greatly reduces the cost of information collection and storage. As a new theory of the field of signal processing,CS attracted widely attention from domestic and foreign scholars, research institutions and big company when it appeared. This thesis introduces the CS theory in detail and makes a in-depth research for measurement matrix and signal reconstruction algorithm for CS. The main work is as follows:(1) First,three types of commonly used compressed sensing observation matrix are compared. We analyze their strengths and weaknesses, and elaborate the construction method of matrix. In order to get better performance measurement matrix, observation matrix optimization algorithms based on Gram matrix has been studied,mainly Elad method and gradient descent. By reducing the value of the non-diagonal elements of the Gram matix to reduce the correlation between the observation matrix and the sparse matrix, thereby we achieve the purpose of optimizing the observation matrix. Because limitations of gradient descent algorithm for high computational complexity, wo make some improvements for the algorithm by eigenvalue decomposition method and define a new error function. Due to low computational complexity, robustness, The improved algorithm is more suitable for solving large-scale problems. The simulation results show that the improved optimization algorithm is superior to other methods.(2) Secondly,in terms of signal reconstruction algorithm of compressed sensing, we mainly research greedy algorithm which is based on 0l norm, summarize algorithms process of several commonly used algorithms and explain the differences in terms of the atomic update.we highlight the generalized orthogonal matching pursuit algorithm recent, and put forward an adaptive matching pursuit algorithm-generalized adaptive matching pursuit algorithm which is on the basis of the proposed algorithm,.Unlike GOMP with OMP algorithm, the improved algorithm does not need to know when the reconstructed signal sparsity signals, cut the number of atoms in each iteration of choice is determined by the residual rate of decline. The simulation experiments show that the improved algorithm can adapt to the different sparse degree of the signal,have a better reconstruction performance.(3) At last, a new solution is found out to improve the original regularization method, which makes the properties of the algorithm more consistent with the greedy matching pursuit algorithm.And the improved method is applied to the regularized orthogonal matching pursuit(ROMP) algorithm.Experiments show that the new algorithm is better than the original algorithm in the reconstruction accuracy and time.