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<p>As a specialized case of compressed sensing, 1-bit compressed sensing retains only the sign information of linear measurements, thereby achieving extremely low-sampling cost and high sampling speed. It also exhibits stronger robustness against nonlinear distortions and additive noise. The Binary Iterative Hard Thresholding (BIHT) algorithm has been proven efficient for solving 1-bit compressed sensing problems. However, the discontinuity of its hard-thresholding function makes its performance highly sensitive to inaccuracies in the estimated signal sparsity level. An inaccurate sparsity estimate leads to a fixed threshold that can cause significant reconstruction bias. To address this issue, this paper proposes a novel Arctangent-Regularized Binary Iterative Thresholding (ARBIT) algorithm. By introducing an arctangent penalty term, the algorithm constructs a continuously adjustable thresholding function that preserves sparsity while effectively mitigating thresholding-induced bias. The algorithm further incorporates an adaptive parameter updating mechanism and a Nesterov momentum strategy to enhance convergence speed and stability. Experimental results demonstrate that the ARBIT algorithm significantly outperforms traditional iterative thresholding methods on both synthetic and real seismic datasets in terms of support set recovery rate, noise robustness, and reconstruction efficiency. This work provides a viable new solution for efficient compression and high-quality reconstruction of seismic data.</p>

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Arctangent-Regularized Binary Iterative Thresholding for 1-bit compressed sensing with application to seismic data reconstruction

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月2日

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  • Hanyu Li,
  • Ronghuo Dai,
  • Jingyao Hou

摘要

As a specialized case of compressed sensing, 1-bit compressed sensing retains only the sign information of linear measurements, thereby achieving extremely low-sampling cost and high sampling speed. It also exhibits stronger robustness against nonlinear distortions and additive noise. The Binary Iterative Hard Thresholding (BIHT) algorithm has been proven efficient for solving 1-bit compressed sensing problems. However, the discontinuity of its hard-thresholding function makes its performance highly sensitive to inaccuracies in the estimated signal sparsity level. An inaccurate sparsity estimate leads to a fixed threshold that can cause significant reconstruction bias. To address this issue, this paper proposes a novel Arctangent-Regularized Binary Iterative Thresholding (ARBIT) algorithm. By introducing an arctangent penalty term, the algorithm constructs a continuously adjustable thresholding function that preserves sparsity while effectively mitigating thresholding-induced bias. The algorithm further incorporates an adaptive parameter updating mechanism and a Nesterov momentum strategy to enhance convergence speed and stability. Experimental results demonstrate that the ARBIT algorithm significantly outperforms traditional iterative thresholding methods on both synthetic and real seismic datasets in terms of support set recovery rate, noise robustness, and reconstruction efficiency. This work provides a viable new solution for efficient compression and high-quality reconstruction of seismic data.