On the 15th July 2020, Silvia Gazzola from the University of Bath gave a talk on “Iteratively Reweighted FGMRES and FLSQR for sparse reconstruction”.

Krylov subspace methods are powerful iterative solvers for large-scale linear inverse problems, such as those arising in image deblurring and computed tomography. In this talk I will present two new algorithms to efficiently solve L2-Lp regularized problems that enforce sparsity in the solution. The proposed approach is based on building a sequence of quadratic problems approximating the original L2-Lp objective function, and partially solving them using flexible Krylov-Tikhonov methods. These algorithms are built upon a solid theoretical justification for converge, and have the advantage of building a single (flexible) approximation (Krylov) Subspace that encodes regularization through variable “preconditioning’’. The performance of the algorithms will be shown through a variety of numerical examples. This is a joint work with Julianne Chung (Virginia Tech), James Nagy (Emory University) and Malena Sabate Landman (University of Bath).

This talk is part of the CCIMI Seminar series. The talk was recorded and can be watched here.