Stable principal component pursuit via convex analysis

Lei Yin, Ankit Parekh, Ivan Selesnick

Research output: Contribution to journalArticlepeer-review


This paper aims to recover a low-rank matrix and a sparse matrix from their superposition observed in additive white Gaussian noise by formulating a convex optimization problem with a non-separable non-convex regularization. The proposed non-convex penalty function extends the recent work of a multivariate generalized minimax-concave penalty for promoting sparsity. It avoids underestimation characteristic of convex regularization, which is weighted sum of nuclear norm and ℓ1 norm in our case. Due to the availability of convex-preserving strategy, the cost function can be minimized through forward-backward splitting. The performance of the proposed method is illustrated for both numerical simulation and hyperspectral images restoration.

Original languageEnglish (US)
Article number8673650
Pages (from-to)2595-2607
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number10
StatePublished - May 15 2019


  • Principal component analysis
  • convex function
  • optimization

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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