Convex denoising using non-convex tight frame regularization

Ankit Parekh, Ivan W. Selesnick

Research output: Contribution to journalArticlepeer-review


This letter considers the problem of signal denoising using a sparse tight-frame analysis prior. The l1 norm has been extensively used as a regularizer to promote sparsity; however, it tends to under-estimate non-zero values of the underlying signal. To more accurately estimate non-zero values, we propose the use of a non-convex regularizer, chosen so as to ensure convexity of the objective function. The convexity of the objective function is ensured by constraining the parameter of the non-convex penalty. We use ADMM to obtain a solution and show how to guarantee that ADMM converges to the global optimum of the objective function. We illustrate the proposed method for 1D and 2D signal denoising.

Original languageEnglish (US)
Article number7105866
Pages (from-to)1786-1790
Number of pages5
JournalIEEE Signal Processing Letters
Issue number10
StatePublished - Oct 1 2015


  • Analysis model
  • convex optimization
  • non-convex regularization
  • sparse signal
  • tight frame

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics


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