One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measure is available to us. The ground-truth signal is not sparse in many applications yet can be represented in a redundant dictionary. A strong line of research has addressed conventional CS in this signal model, including its extension to one-bit measurements. However, one-bit CS suffers from an extremely large number of required measurements to achieve a predefined reconstruction error level. A common alternative to resolve this issue is to exploit adaptive schemes. We utilize an adaptive sampling strategy to recover dictionary-sparse signals from binary measurements in this work. A multi-dimensional threshold is proposed for this task to incorporate the previous signal estimates into the current sampling procedure. This strategy substantially reduces the required number of measurements for exact recovery. We show that the proposed algorithm considerably outperforms the state-of-the-art approaches through rigorous and numerical analysis.

一位压缩感知 (CS) 是稀疏恢复的高级版本，其中感兴趣的稀疏信号可以从极端量化的测量中恢复。也就是说，只有每个度量的符号可供我们使用。地面实况信号在许多应用中并不稀疏，但可以在冗余字典中表示。一项强有力的研究已经解决了该信号模型中的传统 CS，包括将其扩展到一位测量。然而，一位 CS 需要进行大量测量才能达到预定义的重构误差水平。解决此问题的常见替代方法是利用自适应方案。在这项工作中，我们利用自适应采样策略从二进制测量中恢复字典稀疏信号。为此任务提出了一个多维阈值，以将先前的信号估计纳入当前的采样过程。这种策略大大减少了精确恢复所需的测量次数。我们通过严格的数值分析表明，所提出的算法大大优于最先进的方法。