Sparse Stable Outlier-Robust Signal Recovery Under Gaussian Noise

Kyohei Suzuki, Masahiro Yukawa

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This paper presents a novel framework for sparse robust signal recovery integrating the sparse recovery using the minimax concave (MC) penalty and robust regression called sparse outlier-robust regression (SORR) using the MC loss. While the proposed approach is highly robust against huge outliers, the sparseness of estimates can be controlled by taking into consideration a tradeoff between sparseness and robustness. To accommodate the prior information about additive Gaussian noise and outliers, an auxiliary vector to model the noise is introduced. The remarkable robustness and stability come from the use of the MC loss and the squared \ell {2} penalty of the noise vector, respectively. In addition, the simultaneous use of the MC and squared \ell {2} penalties of the coefficient vector leads to a certain remarkable grouping effect. The necessary and sufficient conditions for convexity of the smooth part of the cost are derived under a certain nonempty-interior assumption via the product space formulation using the linearly-involved Moreau-enhanced-over-subspace (LiMES) framework. The efficacy of the proposed method is demonstrated by simulations in its application to speech denoising under highly noisy environments as well as to toy problems.

Original languageEnglish
Pages (from-to)372-387
Number of pages16
JournalIEEE Transactions on Signal Processing
Publication statusPublished - 2023


  • convex optimization
  • minimax concave function
  • outlier-robust signal recovery
  • Sparse modeling
  • sparse outlier-robust signal recovery

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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