Fast Inverse-Free Sparse Bayesian Learning via Relaxed Evidence Lower Bound Maximization

Huiping Duan, Linxiao Yang, Jun Fang, Hongbin Li

Research output: Contribution to journalArticlepeer-review

70 Scopus citations

Abstract

Sparse Beyesian learning is a popular approach for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless, the sparse Bayesian learning algorithm involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size, which hinders its application to many practical problems even with moderately large datasets. To address this issue, in this letter, we develop a fast inverse-free sparse Bayesian learning method. Specifically, by invoking a fundamental property for smooth functions, we obtain a relaxed evidence lower bound (relaxed-ELBO) that is computationally more amiable than the conventional ELBO used by sparse Bayesian learning. A variational expectation-maximization (EM) scheme is then employed to maximize the relaxed-ELBO, which leads to a computationally efficient inverse-free sparse Bayesian learning algorithm. Simulation results show that the proposed algorithm has a fast convergence rate and achieves lower reconstruction errors than other state-of-the-art fast sparse recovery methods in the presence of noise.

Original languageEnglish
Article number7894261
Pages (from-to)774-778
Number of pages5
JournalIEEE Signal Processing Letters
Volume24
Issue number6
DOIs
StatePublished - Jun 2017

Keywords

  • Compressed sensing
  • inverse-free sparse Bayesian learning (SBL)
  • relaxed evidence lower bound (relaxed-ELBO)

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