Accelerated projected gradient method for linear inverse problems with sparsity constraints

Journal Article (Journal Article)

Regularization of ill-posed linear inverse problems via ℓ1 penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an ℓ1 penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to ℓ1-constraints, using a gradient method, with projection on ℓ1-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration. © 2008 Birkhäuser Boston.

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Fornasier, M; Loris, I

Published Date

  • December 1, 2008

Published In

Volume / Issue

  • 14 / 5-6

Start / End Page

  • 764 - 792

International Standard Serial Number (ISSN)

  • 1069-5869

Digital Object Identifier (DOI)

  • 10.1007/s00041-008-9039-8

Citation Source

  • Scopus