Recently, several promising approximate message passing (AMP) based algorithms have been developed for bilinear recovery with model Y = K k=1 b k A k C + W , where {b k } and C are jointly recovered with known A k from the noisy measurements Y . The bilinear recover problem has many applications such as dictionary learning, self-calibration, compressive sensing with matrix uncertainty, etc. In this work, we propose a new bilinear recovery algorithm based on AMP with unitary transformation and hybrid message passing. It is shown that, compared to the state-of-the-art message passing based algorithms, the proposed algorithm is much more robust and faster, leading to remarkably better performance.
This paper concerns message passing based approaches to sparse Bayesian learning (SBL) with a linear model corrupted by additive white Gaussian noise with unknown variance. With the conventional factor graph, mean field (MF) message passing based algorithms have been proposed in the literature. In this work, instead of using the conventional factor graph, we modify the factor graph by adding some extra hard constraints (the graph looks like being 'stretched'), which enables the use of combined belief propagation (BP) and MF message passing. We then propose a low complexity BP-MF SBL algorithm based on which an approximate BP-MF SBL algorithm is also developed to further reduce the complexity. Thanks to the use of BP, the BP-MF SBL algorithms show their merits compared with state-of-the-art MF SBL algorithms: they deliver even better performance with much lower complexity compared with the vector-form MF SBL algorithm and they significantly outperform the scalar-form MF SBL algorithm with similar complexity.Index Terms-sparse Bayesian learning, message passing, BP-MF.
With a unified belief propagation (BP) and mean field (MF) framework, we propose an iterative message passing receiver, which performs joint channel state and noise precision (the reciprocal of noise variance) estimation and decoding for OFDM systems. The recently developed generalized approximate message passing (GAMP) is incorporated to the BP-MF framework, where MF is used to handle observation factor nodes with unknown noise precision and GAMP is used for channel estimation in the time-frequency domain. Compared to state-of-the-art algorithms in the literature, the proposed algorithm either delivers similar performance with much lower complexity, or delivers much better performance with similar complexity. In addition, the proposed algorithm exhibits fastest convergence.
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