Two-dimensional Inverse-Free Sparse Bayesian Learning for Fast Sparse Reconstruction

Abstract

The invention belongs to the field of signal processing, and specifically relates to a two-dimensional inverse-free sparse Bayesian learning fast sparse reconstruction method, comprising the following steps: S1: perform sparse representation modeling on two-dimensional sparse reconstruction problems; S2: vector Statistical modeling of sparse signal x and vectorized noise n; S3: Solve the posterior probability of vectorized sparse signal x, vectorized variance reciprocal γ and noise variance reciprocal α; S4: update the matrix form Z of auxiliary variables. Compared with the IFSBL method, the method of the present invention directly processes two-dimensional signals, avoids the problem of large matrices caused by vectorization of two-dimensional signals, significantly improves the operation efficiency, and significantly reduces the demand for computing memory; on the other hand, The present invention realizes sparse reconstruction under the framework of statistical signal processing. Compared with non-statistical sparse reconstruction methods, it is easier to obtain the global optimal solution, more robust to noise, and the algorithm performance is not highly dependent on parameter initialization, etc. Advantages, strong engineering practicability.

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

[0065] The present invention will be further described below in conjunction with accompanying drawing:

[0066] figure 1 It is the general processing flow of the present invention.

[0067] A two-dimensional inverse-free sparse Bayesian learning fast sparse reconstruction method described in the present invention comprises the following four steps:

[0068] S1: Sparse representation modeling for two-dimensional sparse reconstruction problems;

[0069] S2: Perform statistical modeling on vectorized sparse signal x and vectorized noise n;

[0070] 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;

[0071] S4: Updating the matrix form Z of the auxiliary variables.

[0072] 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

[0065] The present invention will be further described below in conjunction with accompanying drawing:

[0066] figure 1 It is the general processing flow of the present invention.

[0067] A two-dimensional inverse-free sparse Bayesian learning fast sparse reconstruction method described in the present invention comprises the following four steps:

[0068] S1: Sparse representation modeling for two-dimensional sparse reconstruction problems;

[0069] S2: Perform statistical modeling on vectorized sparse signal x and vectorized noise n;

[0070] 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;

[0071] S4: Updating the matrix form Z of the auxiliary variables.

[0072] 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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