Case Western Reserve University
Title Inverse Problems, Bayesian inference and Sparse Solutions: a big of magic in L2
ABSTRACT: Recasting a linear inverse problems within the Bayesian framework makes it possible to use partial or qualitative information about the solution to improve the computed solution in spite of the inherent ill-posedness of the problem and noise in the data. In this talk we will show how a suitably chosen probabilistic setting can lead to a very efficient algorithm for the recovery of sparse solutions that only requires the solution of a sequence of linear least squares problems. The fast converge rate of the algorithm and its low computational cost will be discussed and illustrated with computed examples.