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<p>Thresholding methods are widely used in signal reconstruction, which aim to recover sparse or compressible original signals from a few linear measurements. Although several existing thresholding algorithms perform well in the recovery of sparse signals, the recovery speed and reconstruction performance still need improvement. To address this issue, Wen et al. proposed a sparse recovery algorithm called pseudo-inverse-based hard-thresholding (PHT), which aims to enhance the efficiency of sparse signal recovery. The well-known restricted isometry property (RIP) of the measurement matrix ensures the convergence and stability of recovery algorithms. Within this framework, this paper proposes two new sufficient conditions, namely <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\delta _{2s}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> </InlineEquation> (where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\gamma =\delta _s\)</EquationSource> </InlineEquation> if <i>s</i> is even, and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\gamma =\delta _{s+1}\)</EquationSource> </InlineEquation> otherwise), for ensuring that the PHT algorithm is able to stably recover sparse signals. To the best of our knowledge, this is the first time that such <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\delta _{2s}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> </InlineEquation> sufficient conditions have been proposed for the PHT algorithm.</p>

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Sufficient Conditions Based on RIC for the PHT Algorithm

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Wenhui Tian,
  • Pengbo Geng

摘要

Thresholding methods are widely used in signal reconstruction, which aim to recover sparse or compressible original signals from a few linear measurements. Although several existing thresholding algorithms perform well in the recovery of sparse signals, the recovery speed and reconstruction performance still need improvement. To address this issue, Wen et al. proposed a sparse recovery algorithm called pseudo-inverse-based hard-thresholding (PHT), which aims to enhance the efficiency of sparse signal recovery. The well-known restricted isometry property (RIP) of the measurement matrix ensures the convergence and stability of recovery algorithms. Within this framework, this paper proposes two new sufficient conditions, namely \(\delta _{2s}\) and \(\gamma \) (where \(\gamma =\delta _s\) if s is even, and \(\gamma =\delta _{s+1}\) otherwise), for ensuring that the PHT algorithm is able to stably recover sparse signals. To the best of our knowledge, this is the first time that such \(\delta _{2s}\) and \(\gamma \) sufficient conditions have been proposed for the PHT algorithm.