TY - GEN
T1 - Bayesian Compressed Sensing with Unknown Measurement Noise Level
AU - Hansen, Thomas Lundgaard
AU - Jørgensen, Peter Bjørn
AU - Pedersen, Niels Lovmand
AU - Manchón, Carles Navarro
AU - Fleury, Bernard Henri
PY - 2013/11
Y1 - 2013/11
N2 - In sparse Bayesian learning (SBL) approximate Bayesian inference is applied to find sparse estimates from observations corrupted by additive noise. Current literature only vaguely considers the case where the noise level is unknown a priori. We show that for most state-of-the-art reconstruction algorithms based on the fast inference scheme noise precision estimation results in increased computational complexity and reconstruction error. We propose a three-layer hierarchical prior model which allows for the derivation of a fast inference algorithm that estimates the noise precision with no complexity increase. Numerical results show that it matches or surpasses other algorithms in terms of reconstruction error.
AB - In sparse Bayesian learning (SBL) approximate Bayesian inference is applied to find sparse estimates from observations corrupted by additive noise. Current literature only vaguely considers the case where the noise level is unknown a priori. We show that for most state-of-the-art reconstruction algorithms based on the fast inference scheme noise precision estimation results in increased computational complexity and reconstruction error. We propose a three-layer hierarchical prior model which allows for the derivation of a fast inference algorithm that estimates the noise precision with no complexity increase. Numerical results show that it matches or surpasses other algorithms in terms of reconstruction error.
U2 - 10.1109/ACSSC.2013.6810248
DO - 10.1109/ACSSC.2013.6810248
M3 - Article in proceeding
SN - 978-1-4799-2388-5
T3 - Asilomar Conference on Signals, Systems and Computers. Conference Record
SP - 148
EP - 152
BT - Proc. 47th Asilomar Conference on Signals, Systems and Computers
PB - IEEE
T2 - Asilomar Conference on Signals, Systems, and Computers
Y2 - 3 November 2013 through 6 November 2013
ER -