Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Sparse bayesian learning and the relevance vector machine
The Journal of Machine Learning Research
Sparse Bayesian learning for basis selection
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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We propose a belief propagation (BP) based sparse Bayesian learning (SBL) algorithm, referred to as the BP-SBL, for sparse signal recovery in large scale compressed sensing problems. BP-SBL is based on a widely-used hierarchical Bayesian model. We convert this model to a factor graph and then apply BP to achieve computational efficiency. The computational complexity of BP-SBL is almost linear with respect to the number of transform coefficients, allowing the algorithms to deal with large scale compressed sensing problems efficiently. Numerical examples are provided to demonstrate the effectiveness of BPSBL.