Newton-Type Optimal Thresholding Algorithms for Sparse Optimization Problems

Nan Meng, Yun-bin Zhao

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Abstract

Sparse signals can be possibly reconstructed by an algorithm which merges a traditional nonlinear optimization method and a certain thresholding technique. Different from existing thresholding methods, a novel thresholding technique referred to as the optimal k-thresholding was recently proposed by Zhao (SIAM J Optim 30(1):31–55, 2020). This technique simultaneously performs the minimization of an error metric for the problem and thresholding of the iterates generated by the classic gradient method. In this paper, we propose the so-called Newton-type optimal k-thresholding (NTOT) algorithm which is motivated by the appreciable performance of both Newton-type methods and the optimal k-thresholding technique for signal recovery. The guaranteed performance (including convergence) of the proposed algorithms is shown in terms of suitable choices of the algorithmic parameters and the restricted isometry property (RIP) of the sensing matrix which has been widely used in the analysis of compressive sensing algorithms. The simulation results based on synthetic signals indicate that the proposed algorithms are stable and efficient for signal recovery.
Original languageEnglish
Number of pages23
JournalJournal of the Operations Research Society of China
Early online date4 Jan 2022
DOIs
Publication statusE-pub ahead of print - 4 Jan 2022

Keywords

  • Compressed sensing
  • Space optimization
  • Newton-type methods
  • Optimal k-thresholding
  • Restricted isometry property

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