I. Dassios, K. Fountoulakis and J. Gondzio
Abstract
In this paper we are concerned with the solution of Compressed Sensing (CS)
problems where the signals to be recovered are sparse in coherent and
redundant dictionaries. We extend the primal-dual Newton Conjugate Gradients
(pdNCG) method in [9] for CS problems. We provide an inexpensive and provably
effective preconditioning technique for linear systems using pdNCG.
Numerical results are presented on CS problems which demonstrate
the performance of pdNCG with the proposed preconditioner compared
to state-of-the-art existing solvers.
Key words: compressed sensing, L1-analysis, total-variation, second-order methods, Newton conjugate gradients.