The Research Of Measurement Matrix Based On Compressed Sensing

Compressed Sensing (CS) is a novel signal sampling theory under the condition that the signal is sparse or compressible. It has the ability of compressing a signal during the process of sampling. In the process of compressed sensing, measurement matrix plays a crucial role in sampling data and reconstructing signal. It is the most important part in compressed sensing area. The author of the paper carried out the following works after studying deeply the compressed sensing and common measurement matrices.The relation between measurement number of measurement matrix and sparsity of signal was researched. The expression of specific relations was given between measurement number of Gaussian measurement matrix and sparsity of signal under the OMP algorithm. The performance among the common measurement matrices was compared. The common random measurement matrices were ordered according to their reconstruction results.In order that there is a better reconstruction result, an improved method was proposed for measurement matrix based on orthogonalization of row vector for matrix. The experiments show that improved measurement matrix is better than the original measurement matrix when used to reconstruct signal. After finding the disadvantages of random measurement matrices, a new direction of deterministic measurement matrix was established.In order to overcome the lack of random measurement matrix, polynomial deterministic measurement matrix was proposed. In this paper, the relation between measurement number of polynomial deterministic measurement matrix and sparsity of signal was researched. A scope of sparsity was given when the polynomial deterministic measurement matrix was proposed, but the scope of sparsity of signal which can be reconstructed with this measurement matrix is bigger than that the author given. At the same time, there are the following disadvantages of polynomial deterministic measurement matrix:the time to construct the measurement matrix is too long, the space to store elements of the measurement matrix is too big and the scope of measurement number is limited. In order to overcome those Shortages, blocked polynomial deterministic matrix was proposed in this paper. Theoretical proof shows the proposed matrix satisfies the RIP of measurement matrix, so this kind of matrix can be used in compressed sensing. The experiments show that the proposed measurement matrix is superior to polynomial deterministic measurement matrix.