The success of the compressed sensing algorithms is based on the observation that if the underlying image is known to be sparse, or nearly black, a good approximation can be found as the minimizer of the ell-1 norm. Bayesian hypermodels using conditionally Gaussian priors provide a competitive alternative, in particular when combined with Krylov subspace iterative solvers. We address both computational and theoretical aspects of the proposed iterative algorithms.

This presentation is part of Minisymposium “MS8 - Krylov Methods in Imaging: Inverse Problems, Data Assimilation, and Uncertainty Quantification (2 parts)”
organized by: Arvind Saibaba (North Carolina State University) , Julianne Chung (Virginia Tech) , Eric de Sturler (Virginia Tech) .

Authors:

Daniela Calvetti (Case Western Reserve University)

Erkki Somersalo (Case Western Reserve University)

Alexander Strang (Case Western Reserve University)

Keywords:

bayesian methods, image reconstruction, inverse problems, numerical linear algebra, statistical inverse estimation methods