An iterative thresholding algorithm for linear inverse problems with a sparsity constraint

Journal Article (Journal Article)

We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary preassigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted of ℓP - penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem. Use of such ℓP- penalized problems with p < 2 is often advocated when one expects the underlying ideal noiseless solution to have a sparse expansion with respect to the basis under consideration. To compute the corresponding regularized solutions, we analyze an iterative algorithm that amounts to a Landweber iteration with thresholding (or nonlinear shrinkage) applied at each iteration step. We prove that this algorithm converges in norm. © 2004 Wiley Periodicals, Inc.

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Defrise, M; De Mol, C

Published Date

  • November 1, 2004

Published In

Volume / Issue

  • 57 / 11

Start / End Page

  • 1413 - 1457

International Standard Serial Number (ISSN)

  • 0010-3640

Digital Object Identifier (DOI)

  • 10.1002/cpa.20042

Citation Source

  • Scopus