Accelerated projected gradient method for linear inverse problems with sparsity constraints

Ignace Loris, Ingrid Daubechies, Massimo Fornasier

Research output: Contribution to journalArticlepeer-review

194 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)764–792
JournalJournal of Fourier Analysis and Applications
Issue number5
Publication statusPublished - 2008


  • Linear inverse problems
  • Sparse recovery
  • Projected gradient method


Dive into the research topics of 'Accelerated projected gradient method for linear inverse problems with sparsity constraints'. Together they form a unique fingerprint.

Cite this