Block sparse signal reconstruction method based on greedy iteration

Abstract

The invention discloses a block sparse signal reconstruction method based on greedy iteration. All components contained in a block sparse signal are reconstructed from the point of view of geometric projection, and a produced estimated signal is corrected repeatedly in a backtracking check mode to ensure a high reconstruction probability. In the specific implementation process of the block sparse signal reconstruction method, the reconstruction process is divided into a plurality of stages; the signal sparsity is approximated stage by stage; partial signal components will be estimated at each stage until the correct sparsity is estimated; multiple iterations will be performed at each stage; the neighborhood points of all the current estimated values are analyzed based on the characteristic of segmental continuous distribution of non-zero elements of the block sparse signal, and therefore, the position of the block is located and the purpose of reconstruction is achieved.

Description

technical field [0001] The invention belongs to the technical field of compressed sensing, and more specifically relates to a method for reconstructing block sparse signals based on greedy iteration. Background technique [0002] Compressed sensing is a sampling method for sparse signals, which can complete signal compression with high efficiency while sampling. The significance of compressing a sparse signal is that the sparse signal contains only a small number of non-zero elements, and the redundancy can be reduced through compression. Specifically, compressed sensing obtains a low-dimensional sample from a high-dimensional sparse signal through a non-orthogonal projection value, i.e. y m×1 = Φ m×N x N×1 ,like figure 1 As shown, let x be a sparse signal with a length of N, Φ be a sampling matrix of M×N, and the number of rows of the matrix is ​​much smaller than the number of columns, so that the dimension of the sampling value y is much smaller than the dimension of ...

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Problems solved by technology

Therefore, the algorithm used to restore any sparse signal can actually deal with block sparse signals, but the efficiency is lower than that of the above algorithm, because it does not use any prior signal

The restoration of any sparse signal is mainly composed of two types of algorithms. One is convex optimization. Its advantage is that the number of samples required is small, and strict mathematical conditions can be given to indicate under what circumstances it can be restored without distortion. The disadvantage is that the amount of calculation is extremely large.

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