Sparse signal approximation via nonseparable regularization

Ivan Selesnick, Masoud Farshchian

Research output: Contribution to journalArticlepeer-review


The calculation of a sparse approximate solution to a linear system of equations is often performed using either L1-norm regularization and convex optimization or nonconvex regularization and nonconvex optimization. Combining these principles, this paper describes a type of nonconvex regularization that maintains the convexity of the objective function, thereby allowing the calculation of a sparse approximate solution via convex optimization. The preservation of convexity is viable in the proposed approach because it uses a regularizer that is nonseparable. The proposed method is motivated and demonstrated by the calculation of sparse signal approximation using tight frames. Examples of denoising demonstrate improvement relative to L1 norm regularization.

Original languageEnglish (US)
Article number7857076
Pages (from-to)2561-2575
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number10
StatePublished - May 15 2017


  • Sparse signal model
  • convex function
  • denoising
  • optimization
  • sparse approximation

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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