An iteratively reweighted least squares algorithm for sparse regularization

Book Section

We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the idea of iteratively reweighted least squares, reducing the minimization at every iteration step to that of a functional including only ℓ2 -norms. This amounts to smoothing of the absolute value function that appears in the generalized sparsity promoting penalty we consider, with the smoothing becoming iteratively less pronounced. We demonstrate that the sequence of iterates of our algorithm converges to a limit that minimizes the original functional.

Full Text

Duke Authors

Cited Authors

  • Voronin, S; Daubechies, I

Published Date

  • January 1, 2017

Volume / Issue

  • 693 /

Book Title

  • Contemporary Mathematics

Start / End Page

  • 391 - 411

Digital Object Identifier (DOI)

  • 10.1090/conm/693/13941

Citation Source

  • Scopus