Stable principal component pursuit via convex analysis

Lei Yin, Ankit Parekh, Ivan Selesnick

Research output: Contribution to journalArticle

Abstract

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 ℓ 1 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
Volume67
Issue number10
DOIs
StatePublished - May 15 2019

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Convex optimization
Image reconstruction
Cost functions
Availability
Computer simulation

Keywords

  • convex function
  • optimization
  • Principal component analysis

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Stable principal component pursuit via convex analysis. / Yin, Lei; Parekh, Ankit; Selesnick, Ivan.

In: IEEE Transactions on Signal Processing, Vol. 67, No. 10, 8673650, 15.05.2019, p. 2595-2607.

Research output: Contribution to journalArticle

Yin, Lei ; Parekh, Ankit ; Selesnick, Ivan. / Stable principal component pursuit via convex analysis. In: IEEE Transactions on Signal Processing. 2019 ; Vol. 67, No. 10. pp. 2595-2607.
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