Method for constructing block orthogonal symmetric toeplitz matrices (OSTM) compression measurement matrix
A technology of measurement matrix and construction method, applied in complex mathematical operations, etc., can solve problems such as high cost and difficulty in physical realization of random measurement matrix
Inactive Publication Date: 2014-03-19
TIANJIN UNIV
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[0012] Aiming at the difficulties in the physical realization of the random measurement matrix in the prior art and the high cost, the present invention proposes a method for constructing the block-based OSTM compressed measurement matrix. A Block Orthogonal Symmetrical Toeplitz(OSTM) Measurement Matrix Construction Method
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[0028] The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings.
[0029] From the analysis of matrix construction, it is obtained that the number of independent variables in the block cyclic Toeplitz matrix is (2n-1)N, and because the OSTM matrix has symmetric characteristics, the number of independent variables in the constructed measurement matrix is nN / 2, about 1 / 4 of the former. Therefore, when the size of the required measurement matrix is large, the number of independent elements of the constructed matrix is greatly reduced, thereby reducing the storage capacity and improving the operation rate. In addition, constructing the measurement matrix according to the block-by-block loop structure takes advantage of the pseudo-cycle feature, which is easier to implement in hardware than the measurement matrix constructed simply by using element loops.
[0030] In order to verif...
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The invention discloses a method for constructing a block orthogonal symmetric toeplitz matrices (OSTM) compression measurement matrix based on OSTM design and a block circulant matrix structure. The method comprises the following steps of 1, generating N square matrixes phij (1<=j<=N) of n*n according to a construction method of an OSTM matrix; 2, taking each of phij (1<=j<=N) as an element, and arranging the N phij in order to form a block row vector (phiN, phiN-1, ..., phi1); 3, taking the block row vector (phiN, phiN-1, ..., phi1) as the first line of a block circulant measurement matrix phi, performing block circulant according to a generation mode of a circulant matrix to generate residual N-1 vectors and finally forming a block circulant measurement matrix square matrix phi of Nn*Nn; 4, drawing M row vectors from the block circulant measurement matrix square matrix phi randomly to obtain the final measurement matrix. Compared with the prior art, hardware implementation is easy, the number of independent variables is lowered, and storage space and operation time can be reduced.
Description
technical field [0001] The invention belongs to the technical field of computer image processing, in particular to a computer image compression sensing imaging method. Background technique [0002] In the computer image compression sensing imaging process, the measurement matrix plays a vital role in the signal acquisition and reconstruction. At present, it has been proved that random measurement matrices, including Gaussian random matrix and Bernoulli random matrix, satisfy the RIP characteristics and can be used as universal measurement matrices. However, due to the strong randomness, this kind of measurement matrix is not practical no matter in terms of hardware implementation or reconstruction algorithm. In order to facilitate hardware implementation and algorithm optimization, the deterministic measurement matrix is an important type of matrix that pushes compressed sensing to practicality. Orthogonal Symmetric Toeplitz Matrices (OSTM) proposed by Bottcher is a re...
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Inventor 杨爱萍张金霞栗改董翠翠
Owner TIANJIN UNIV