Compressed sensing (CS) is a technique which uses fewer measurements than dictated by the Nyquist sampling theorem. The traditional CS with linear measurements achieves effective recovery, but it suffers from large bit consumption due to the precision required by those measurements. Then, the one-bit CS with binary measurements is proposed to save the bit budget, but it is infeasible when the energy information of signals is not available as a prior knowledge. Subsequently, the hybrid CS which combines traditional CS and one-bit CS appears, striking a balance between the pros and cons of both types of CS. Given that one-bit CS is optimal for the direction estimation of signals under noise with a fixed bit budget and that traditional CS is able to provide residue information and estimated signals, we focus on the design of greedy algorithms, which consist of the main steps of support detection and recovered signal updates, for hybrid CS in this paper. We propose two greedy algorithms for hybrid CS, with traditional CS offering signal estimates and updated residues, which help one-bit CS detect the support iteratively. Then, we provide a theoretical analysis of the error bound between the normalized original signal and the normalized estimated signal. Numerical results demonstrate the efficacy of the proposed greedy algorithms for hybrid CS in noisy environments.

中文翻译：

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混合压缩感知的贪心算法

压缩感知 (CS) 是一种使用比奈奎斯特采样定理所规定的更少的测量值的技术。具有线性测量的传统 CS 实现了有效的恢复，但由于这些测量所需的精度，它会遭受大量比特消耗。然后，提出了具有二进制测量的一位 CS 以节省位预算，但当信号的能量信息不可用作为先验知识时，这是不可行的。随后，结合传统CS和一位CS的混合CS出现，在两种类型的CS的优缺点之间取得了平衡。鉴于一位 CS 对于具有固定比特预算的噪声下信号的方向估计是最佳的，并且传统 CS 能够提供残差信息和估计信号，我们专注于贪婪算法的设计，本文包括支持检测和恢复信号更新的主要步骤，用于混合 CS。我们为混合 CS 提出了两种贪婪算法，传统 CS 提供信号估计和更新的残差，这有助于一位 CS 迭代检测支持。然后，我们提供了归一化原始信号和归一化估计信号之间的误差界限的理论分析。数值结果证明了所提出的贪婪算法在嘈杂环境中用于混合 CS 的有效性。我们提供了归一化原始信号和归一化估计信号之间的误差界限的理论分析。数值结果证明了所提出的贪婪算法在嘈杂环境中用于混合 CS 的有效性。我们提供了归一化原始信号和归一化估计信号之间的误差界限的理论分析。数值结果证明了所提出的贪婪算法在嘈杂环境中用于混合 CS 的有效性。