Compressive sensing method based on scale-free complex network LDPC code

Abstract

The invention provides a compressive sensing method based on a scale-free complex network LDPC (Low Density Parity Check) code, which comprises two processes of the sensing matrix construction and the signal reconstruction arithmetic. The method is characterized by comprising the following steps: sparsely representing a signal x by adopting appropriate basis function, constructing a check matrix H of an irregular low complexity and scale-free network LDPC code, taking the check matrix H of the scale-free network LDPC code as the sensing matrix phi of the compressive sensing arithmetic, calculating the measured value y which equals to phi x, and reconstructing an original signal from the measured value by utilizing a belief propagation (BP) decoding algorithm. The method has the advantages that the constructed scale-free network LDPC code with good performance is applied to the compressive sensing; compressive sensing signal reconstruction is realized by utilizing the decoding method; the method can be applied to the fields such as signal processing, image processing, error correction coding and radar imaging; and the application prospect is wide.

Description

technical field [0001] The present invention relates to the field of signal processing, more specifically, to the technical field of sampling and signal reconstruction in signal processing. Background technique [0002] Compressive Sensing (CS) is a new and rapidly developing theory of information acquisition and processing that has emerged in recent years. The problem of compressed sensing is to recover the N-dimensional signal x∈R from the M-dimensional linear measurement y=Φx N , where y∈R M , Φ is a known M×N matrix. When M<<N, the linear system is underdetermined. But if the signal x is very sparse, then even if M<<N, compressed sensing can reconstruct the signal x from few linear measurements y. Because of its performance superior to the traditional sampling theorem and signal reconstruction, compressed sensing has been paid attention to and extensively studied by many researchers. The research of compressed sensing mainly focuses on three aspects, one...

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Problems solved by technology

[0004] The signal reconstruction method based on coding theory is also applied to the signal reconstruction of compressed sensing, but in some designs, the sensing matrix is ​​dense, so the computational complexity is high; Density Parity Check, LDPC) code-aware matrix, but using regular LDPC codes

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