Vector Approximate Message Passing with Sparse Bayesian Learning for Gaussian Mixture Prior

Chengyao Ruan

doi:10.23919/JCC.2023.00.005

Vector Approximate Message Passing with Sparse Bayesian Learning for Gaussian Mixture Prior

2023-05-01

10

PRE

AI

DOI：10.23919/JCC.2023.00.005

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Compressed sensing (CS) aims for seek-ing appropriate algorithms to recover a sparse vec-tor from noisy linear observations. Currently, various Bayesian-based algorithms such as sparse Bayesian learning (SBL) and approximate message passing (AMP) based algorithms have been proposed. For SBL, it has accurate performance with robustness while its computational complexity is high due to ma-trix inversion. For AMP, its performance is guaran-teed by the severe restriction of the measurement ma-trix, which limits its application in solving CS prob-lem. To overcome the drawbacks of the above algo-rithms, in this paper, we present a low complexity al-gorithm for the single linear model that incorporates the vector AMP (VAMP) into the SBL structure with expectation maximization (EM). Specifically, we ap-ply the variance auto-tuning into the VAMP to imple-ment the E step in SBL, which decrease the iterations that require to converge compared with VAMP-EM al-gorithm when using a Gaussian mixture (GM) prior. Simulation results show that the proposed algorithm has better performance with high robustness under var-ious cases of difficult measurement matrices.

Keyword:

sparse Bayesian learning

approximate message passing

compressed sensing

expectation propagation

Vector Approximate Message Passing with Sparse Bayesian Learning for Gaussian Mixture Prior

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