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Guarantees of Fast Band Restricted Thresholding Algorithm for Low-Rank Matrix Recovery Problem

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  • Fujun Zhao
  • Jigen Peng
  • Kai Sun
  • Angang Cui

Abstract

Affine matrix rank minimization problem is a famous problem with a wide range of application backgrounds. This problem is a combinatorial problem and deemed to be NP-hard. In this paper, we propose a family of fast band restricted thresholding (FBRT) algorithms for low rank matrix recovery from a small number of linear measurements. Characterized via restricted isometry constant, we elaborate the theoretical guarantees in both noise-free and noisy cases. Two thresholding operators are discussed and numerical demonstrations show that FBRT algorithms have better performances than some state-of-the-art methods. Particularly, the running time of FBRT algorithms is much faster than the commonly singular value thresholding algorithms.

Suggested Citation

  • Fujun Zhao & Jigen Peng & Kai Sun & Angang Cui, 2020. "Guarantees of Fast Band Restricted Thresholding Algorithm for Low-Rank Matrix Recovery Problem," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-14, April.
    • Handle: RePEc:hin:jnlmpe:9578168
    DOI: 10.1155/2020/9578168
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