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

TL;DR

This paper introduces a preconditioning technique for a primal-dual Newton conjugate gradients method, improving the efficiency of solving compressed sensing problems with sparse signals in redundant dictionaries.

Contribution

It extends the pdNCG method with a new preconditioner that enhances computational performance for compressed sensing problems involving complex dictionaries.

Findings

Preconditioned pdNCG outperforms existing solvers in numerical tests.

The proposed preconditioner is inexpensive and effective.

Results demonstrate faster convergence and improved accuracy.

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 a primal-dual Newton Conjugate Gradients (pdNCG) method 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.