TY - JOUR
T1 - Fast Inverse-Free Sparse Bayesian Learning via Relaxed Evidence Lower Bound Maximization
AU - Duan, Huiping
AU - Yang, Linxiao
AU - Fang, Jun
AU - Li, Hongbin
N1 - Publisher Copyright:
© 1994-2012 IEEE.
PY - 2017/6
Y1 - 2017/6
N2 - 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.
AB - 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.
KW - Compressed sensing
KW - inverse-free sparse Bayesian learning (SBL)
KW - relaxed evidence lower bound (relaxed-ELBO)
UR - http://www.scopus.com/inward/record.url?scp=85027376768&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85027376768&partnerID=8YFLogxK
U2 - 10.1109/LSP.2017.2692217
DO - 10.1109/LSP.2017.2692217
M3 - Article
AN - SCOPUS:85027376768
SN - 1070-9908
VL - 24
SP - 774
EP - 778
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
IS - 6
M1 - 7894261
ER -