Two-dimensional inversion-free sparse Bayesian learning rapid sparse reconstruction method

Abstract

The invention belongs to the field of signal processing, and particularly relates to a two-dimensional inversion-free sparse Bayesian learning rapid sparse reconstruction method. The method comprisesthe following steps of: S1: carrying out sparse representation modeling on a two-dimensional sparse reconstruction problem; S2: performing statistical modeling on a vectorized sparse signal x and vectorized noise n; S3: solving the posterior probability of the vectorized sparse signal x, the vectorized inverse variance gamma and the noise inverse variance alpha; and S4: updating the matrix form Zof the auxiliary variables. Compared with the IFSBL method, the two-dimensional inversion-free sparse Bayesian learning rapid sparse reconstruction method has the advantages that the two-dimensional signals are directly processed, the problem that a large matrix is generated due to vectorization of the two-dimensional signals is avoided, the operation efficiency is obviously improved, and the requirement on a calculation memory is obviously reduced; and on the other hand, sparse reconstruction is realized under a statistical signal processing frame, and compared with a non-statistical sparse reconstruction method, the method has the advantages of being easier to obtain a global optimal solution, higher in noise robustness, lower in dependence degree of algorithm performance on parameter initialization and the like, and the engineering practicability is high.

Description

technical field

[0001] The invention belongs to the field of signal processing, in particular to a two-dimensional inverse-free sparse Bayesian learning (2Dimentional Inverse-Free Sparse Bayesian Learning, 2D-IFSBL) fast sparse reconstruction method. Background technique

[0002] Sparse reconstruction is the core of compressed sensing technology, which can accurately reconstruct sparse signals from incomplete observation data. After continuous development, sparse reconstruction technology has been widely used in medical image processing, computer vision, radar imaging and other fields. Classical sparse reconstruction algorithms include l1 regularization, Basis Pursuit (BP), Orthogonal Matching Pursuit (OMP), Sparse Bayesian Learning (SBL), etc. Among them, the SBL method is to solve the sparse reconstruction problem under the framework of statistical theory, and to model and solve the statistical priori and posteriori of the observed signal, sparse signal and noise signal, ...

Examples

Embodiment Construction

[0066] The present invention will be further described below in conjunction with accompanying drawing:

[0067] figure 1 It is the general processing flow of the present invention.

[0068] A two-dimensional inverse-free sparse Bayesian learning fast sparse reconstruction method described in the present invention comprises the following four steps:

[0069] S1: Sparse representation modeling for two-dimensional sparse reconstruction problems;

[0070] S2: Perform statistical modeling on vectorized sparse signal x and vectorized noise n;

[0071] S3: Solve the posterior probability of the vectorized sparse signal x, the reciprocal of the vectorized variance γ and the reciprocal of the noise variance α;

[0072] S4: Updating the matrix form Z of the auxiliary variables.

[0073] Using simulation data to conduct experiments, compare the method of the present invention with the IFSBL method (Duan H, Yang L, Fang J, and Li H. Fast Inverse-Free Sparse Bayesian Learning via Relax...

technical field

[0001] The invention belongs to the field of signal processing, in particular to a two-dimensional inverse-free sparse Bayesian learning (2Dimentional Inverse-Free Sparse Bayesian Learning, 2D-IFSBL) fast sparse reconstruction method. Background technique

[0002] Sparse reconstruction is the core of compressed sensing technology, which can accurately reconstruct sparse signals from incomplete observation data. After continuous development, sparse reconstruction technology has been widely used in medical image processing, computer vision, radar imaging and other fields. Classical sparse reconstruction algorithms include l1 regularization, Basis Pursuit (BP), Orthogonal Matching Pursuit (OMP), Sparse Bayesian Learning (SBL), etc. Among them, the SBL method is to solve the sparse reconstruction problem under the framework of statistical theory, and to model and solve the statistical priori and posteriori of the observed signal, sparse signal and noise signal, ...

Examples

Embodiment Construction

[0066] The present invention will be further described below in conjunction with accompanying drawing:

[0067] figure 1 It is the general processing flow of the present invention.

[0068] A two-dimensional inverse-free sparse Bayesian learning fast sparse reconstruction method described in the present invention comprises the following four steps:

[0069] S1: Sparse representation modeling for two-dimensional sparse reconstruction problems;

[0070] S2: Perform statistical modeling on vectorized sparse signal x and vectorized noise n;

[0071] S3: Solve the posterior probability of the vectorized sparse signal x, the reciprocal of the vectorized variance γ and the reciprocal of the noise variance α;

[0072] S4: Updating the matrix form Z of the auxiliary variables.

[0073] Using simulation data to conduct experiments, compare the method of the present invention with the IFSBL method (Duan H, Yang L, Fang J, and Li H. Fast Inverse-Free Sparse Bayesian Learning via Relax...

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