SCAIM Seminar: Hui Huang (UBC)

We address the problem of prior matrix estimation for the solution of L1-regularized ill-posed inverse problems. Considering a Bayesian viewpoint, we show that such a matrix can be regarded as an influence matrix in a multivariate L1-Laplace density function.

Assuming a training set is given, the prior matrix design problem is cast as a maximum likelihood term with the addition of a sparsity-inducing term. This formulation results in an unconstrained and non-convex optimization problem. Memory requirements as well as computation of the nonlinear, non-smooth sub-gradient equations are prohibitive for large-scale problems. In this study we introduce an iterative algorithm developed for efficient prior design for such large problems. We further demonstrate that the solution of ill-posed inverse problems by incorporation of L1-regularization using the learned prior matrix performs generally better than commonly used regularization techniques where the prior matrix is chosen a-priori.