Hui Huang
Optimal Estimation for Signal Priors

University of British Columbia
201-2366 Main Mall
Vancouver
BC V6T1Z4 Canada
hhuang@eos.ubc.ca
Eldad Haber

We consider the problem of estimating signal priors, which are used in the $\ell_1$-regularization and the resulting inverse problem has a stabilized solution. From a Bayesian viewpoint, we first define a multivariate $\ell_1$-Laplace density function and then solve a maximum likelihood problem with an added $\ell_1$-norm penalty term. The problem as formulated is convex but the memory requirements and the nonlinear non-smooth sub-gradient equations are prohibitive for large-scale problems. We develop an iterative algorithm to efficiently solve such large problems and demonstrate the selected priors generally behave better than those commonly used ones in the signal processing.