Generalized Arnoldi-Tikhonov method for sparse reconstruction

Silvia Gazzola, James G. Nagy

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)

Abstract

This paper introduces two new algorithms, belonging to the class of Arnoldi- Tikhonov regularization methods, which are particularly appropriate for sparse reconstruction. The main idea is to consider suitable adaptively defined regularization matrices that allow the usual 2- norm regularization term to approximate a more general regularization term expressed in the p-norm, p = 1. The regularization matrix can be updated both at each step and after some iterations have been performed, leading to two different approaches: the first one is based on the idea of the iteratively reweighted least squares method and can be obtained considering flexible Krylov subspaces; the second one is based on restarting the Arnoldi algorithm. Numerical examples are given in order to show the effectiveness of these new methods, and comparisons with some other already existing algorithms are made.

Original languageEnglish
Pages (from-to)B225-B247
Number of pages23
JournalSIAM Journal on Scientific Computing
Volume36
Issue number2
Early online date3 Apr 2014
DOIs
Publication statusPublished - 31 Dec 2014

Keywords

  • Arnoldi method
  • Inverse problems
  • Krylov subspace
  • Preconditioning
  • Regularization
  • Sparse reconstruction
  • Total variation

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

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