Method for realizing sparse signal recovery on CPU (Central Processing Unit) based on OMP (Orthogonal Matching Pursuit) algorithm

Abstract

The invention discloses a method for realizing sparse signal recovery on a CPU (Central Processing Unit) based on an OMP (Orthogonal Matching Pursuit) algorithm. The method comprises the following steps of: generating an observation matrix on the CPU, and selecting a column with the greatest relevancy to the residual in the observation matrix to complement a basis matrix, wherein the residual is the difference between the observations generated by an actual observation signal and an estimation signal, and the basis matrix is a matrix formed by nonzero element index values in corresponding column vectors in the observation matrix; by use of a method of least squares, estimating the nonzero elements of an original signal on the basis matrix of the kth step; continuing to select the column with the greatest relevancy to the residual in the observation matrix on the CPU to complement the basis matrix, when the variance between the real observation and the estimation observation is lower than a specified threshold, ending the iterative operation. The method provided by the invention has the following advantages: in parallel realization of the OMP algorithm by the CPU, the advantages of low computational complexity and high convergence rate of the OMP algorithm are combined, and simultaneously, the characteristic of remarkable acceleration performance of the CPU algorithm to the vector computation is fully used, and the running speed of the sparse recovery algorithm is improved effectively.

Description

technical field [0001] The invention belongs to the technical field of signal processing, and in particular relates to a method for realizing sparse signal restoration on a GPU based on an OMP algorithm. Background technique [0002] In recent years, compressive sensing theory has received widespread attention, which shows that under the premise that the signal satisfies sparsity, the original signal can be completely restored by sampling the data with a sampling frequency much smaller than the Nyquist sampling rate. Compressed sensing is formulated with the following mathematical expression: [0003] For the original signal x∈R N , through the observation matrix Φ∈R M×N , get the observation vector y∈R M : [0004] y=Φx (1) [0005] Where M<<N, the number of significant elements in x is S, and S<<N. The research of CS theory is: given the observation y, estimate the sparsest solution x that satisfies the formula (1), that is, to find a Satisfy: [0006]...

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Problems solved by technology

The disadvantage of this method is that the convergence speed of the MP algorithm itself is slow, and the probability of successful recovery is small when the basis correlation is large.

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