Measurement matrix design method based on LDPC matrix

Abstract

The invention discloses a measurement matrix design method based on an LDPC matrix. The method comprises the following steps: the step one in which the number L of continuous '1' at the beginning of the first row of the matrix is determined at first, and positions of '1' in the following row of the matrix are subjected to translation to the right for L positions successively according to positions of '1' in the previous row so as to ensure that the positions of '1' between every two rows or every two columns in a cycle submatrix are different to construct the cycle submatrix; the step two in which required rows or columns are randomly selected from the cycle submatrix to construct a measurement matrix based on the LDPC matrix; and the step three in which four-side loops are found in the whole matrix through searches of a limited number, and the four-side loops are eliminated to construct the measurement matrix based on the LDPC matrix. The measurement matrix inherits advantages, such as good sparsity, small column correlation values, etc., of the LDPC matrix, and at the same time, the shortage that optimal d values (the average number of '1' in each column) need to be determined for different dimensions of measurement matrixs in advance when the LDPC matrix is used as the compression sensing measurement matrix can be overcome. The matrix has advantages of good sparsity, simple structure, good orthogonality, easy hardware implementation and good reconstruction effect.

Description

technical field [0001] The invention relates to the technical field of image compression sensing, in particular to a method for designing a measurement matrix in the field of compressed sensing. Background technique [0002] In recent years, the Compressive Sensing theory (Compressive Sensing, CS) proposed by Candes and Donoho et al. provides theoretical support for new image acquisition and compression processing. The high-dimensional or compressible high-dimensional signal is projected onto a low-dimensional space, and then the original signal or image is reconstructed with high probability from a small number of projections by solving an optimization problem. The core idea of ​​CS theory is to combine compression and sampling, which breaks through the bottleneck of Shannon's sampling theorem, that is, only a small number of sample points can accurately reconstruct the original image. [0003] The design of the measurement matrix is ​​a crucial link in the design process ...

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Problems solved by technology

[0007] However, in the existing measurement matrix design methods based on LDPC codes, for measurement matrices with different dimensions, it is necessary to determine the d value that can optimize the performance before each matrix construction. The design process is cumbersome, which is not conducive to practical applications.

And the LDPC matrix requires at least three "1"s in each column, and its sparsity needs to be further improved

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