A Preconditioner for a Primal-dual Newton Conjugate Gradients Method for Compressed Sensing Problems

Technical Report ERGO-14-021

I. Dassios, K. Fountoulakis and J. Gondzio

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.

PDF ERGO-14-021.pdf.
Final SISC version

Written: December 28, 2014, revised July 2, 2015.
SIAM Journal on Scientific Computing 37 (2015) A2783--A2812.
Published online November 24, 2015.

Related Software:
pdNCG primal-dual Newton Conjugate Gradients.