Improved sparse low-rank matrix estimation

Ankit Parekh, Ivan W. Selesnick

Research output: Contribution to journalArticlepeer-review


We address the problem of estimating a sparse low-rank matrix from its noisy observation. We propose an objective function consisting of a data-fidelity term and two parameterized non-convex penalty functions. Further, we show how to set the parameters of the non-convex penalty functions, in order to ensure that the objective function is strictly convex. The proposed objective function better estimates sparse low-rank matrices than a convex method which utilizes the sum of the nuclear norm and the ℓ1 norm. We derive an algorithm (as an instance of ADMM) to solve the proposed problem, and guarantee its convergence provided the scalar augmented Lagrangian parameter is set appropriately. We demonstrate the proposed method for denoising an audio signal and an adjacency matrix representing protein interactions in the ‘Escherichia coli’ bacteria.

Original languageEnglish (US)
Pages (from-to)62-69
Number of pages8
JournalSignal Processing
StatePublished - Oct 1 2017


  • Convex optimization
  • Low-rank matrix
  • Non-convex regularization
  • Sparse matrix
  • Speech denoising

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering


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