Research On The Measurement Matrix And Reconstruction Algorithm In Compressed Sensing

With the rapid development of information technology, the pressure is great in signal processing system because the data need to deal with is increasing greatly. In recent years, the compressed sensing had been proposed as a solution to relieve the pressure. If the signal is sparse or compressible or sparse in the transform domain, it could be projected from high dimensional to low dimensional in the transform domain with measurement matrix that nearly has no coherence with the sparse basis. We can reconstruct the original signal accurately from projection in low dimensional with high probability by solving optimization problem. Measurement matrix is the key point to compressed sensing because it guarantees that measurements in low dimensional include enough information of the original signal, in this sense, measurement matrix made it possible to reconstruct the signal. The reconstruction algorithm would have a influence on the accuracy of reconstructed signal directly. In this paper, we researched on reconstruction algorithm and the optimization of measurement matrix, the main work is as follows:1. Some reconstruction algorithms and two principles of the measurement matrix in compressed sensing are described. In terms of precision and compute complexity, the experiment make a comparison with several common measurement matrixs using Orthogonal Matching Pursuit and Gradient pursuit.2.We study the influence of QR decomposition and SVD decomposition and orthogonalization of row vector to the minimum singular value of matrix. We also analyse the relationship between the independence of the columns, orthogonalization of row vector and the minimum singular value in matrix. Experimental results show that these methods improve the quality of the reconstruction signal because of increasing the minimum singular value of measurement matrix.3. The optimization algorithm of Garm matrix improve the precision of reconstruction signal by means of decreasing the mutual coherence between measurement matrix and sparse basis. However it did not consider the independence of the column vector and the orthogonality of the row vector in measurement matrix. Combining these ideas with the optimization algorithm of Garm matrix, the modified algorithm based on Garm matrix is proposed. Experimental results demonstrate the effectiveness of this algorithm.4. The optimization algorithm of gradient-based Garm matrix decrease the mutual coherence between measurement matrix and sparse basis by means of the Garm matrix approximating the deformation matrix of equiangular tight frame. However it did not consider the independence of the column vector and the orthogonality of the row vector in measurement matrix. Combining these ideas with the optimization algorithm of gradient-based Garm matrix, the modified algorithm gradient-based Garm matrix is proposed. Experimental results demonstrate the effectiveness of this algorithm.5. The Block-based Compressed Sensing with Smoothed Projected Landweber(BCS-SPL) reconstruction algorithm has been studied. The Multiscale BCS-SPL(MS-BCS-SPL) reconstruction algorithm has been analysed. The coefficient of energy is more concentrated in Discrete Cosine Transform(DCT) than discrete wavelet transform(DWT), a band Compressed Sensing with Smooth Projection Landweber reconstruction algorithm base on DCT is proposed. Experimental results indicate that the proposed reconstruction algorithm effectively improves the image quality.