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<p>In this paper, we introduce the well-known Nesterov’s acceleration strategy to enhance the performance of Hard Thresholding Pursuit (HTP) for solving sparse signal recovery problems. The new algorithm, called Nesterov’s Accelerated Hard Thresholding Pursuit (NAHTP), retains the same low computational complexity as HTP. We establish convergence analysis and provide iteration step estimates by utilizing the restricted isometry property of measurement matrices. Specifically, a sparse vector can be exactly recovered within a number of iterative steps proportional to the sparsity degree, and if further enhancing the restricted isometry condition, the iterative process can be terminated in at most as many steps as the sparsity degree. The effectiveness of NAHTP is validated through numerical simulations on both random instances and synthetic signals.</p>

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Nesterov’s Accelerated Hard Thresholding Pursuit Algorithms for Compressed Sensing

  • 期刊论文

  • 发表日期：

    2025年9月28日

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  • Liping Geng,
  • Yongchao Liu,
  • Jingyong Tang,
  • Jinchuan Zhou

摘要

In this paper, we introduce the well-known Nesterov’s acceleration strategy to enhance the performance of Hard Thresholding Pursuit (HTP) for solving sparse signal recovery problems. The new algorithm, called Nesterov’s Accelerated Hard Thresholding Pursuit (NAHTP), retains the same low computational complexity as HTP. We establish convergence analysis and provide iteration step estimates by utilizing the restricted isometry property of measurement matrices. Specifically, a sparse vector can be exactly recovered within a number of iterative steps proportional to the sparsity degree, and if further enhancing the restricted isometry condition, the iterative process can be terminated in at most as many steps as the sparsity degree. The effectiveness of NAHTP is validated through numerical simulations on both random instances and synthetic signals.