1-Bit压缩感知盲重构算法

1-Bit压缩感知(CS)是压缩感知理论的一个重要分支。该领域中二进制迭代硬阈值(BIHT)算法重构精度高且一致性好，是一种有效的重构算法。该文针对BIHT算法重构过程需要信号稀疏度为先验信息的问题，提出一种稀疏度自适应二进制迭代硬阈值算法，简称为SABIHT算法。该算法修正了BIHT算法，首先通过自适应过程自动调节硬阈值参数，然后利用测试条件估计信号的稀疏度，最终实现不需要确切信号稀疏度的1-Bit压缩感知盲重构。理论分析和仿真结果表明，该算法较好地实现了未知信号稀疏度的精确重建，并且与BIHT算法相比重构精度及算法复杂度均相当。

A Blind 1-Bit Compressive Sensing Reconstruction Method

1-Bit Compressive Sensing (CS) is an important branch of standard CS. The existing 1-Bit CS algorithm-Binary Iterative Hard Thresholding (BIHT) can perfectly recovery signals with high precision and consistency, which requires exact sparsity level in the recovery phase. Considering this problem, a new Sparsity Adaptive Binary Iterative Hard Thresholding (SABIHT) algorithm without prior information of the sparsity is proposed by modifying the BIHT algorithm. By using the adaptive process of automatically adjusting the hard threshold parameters and test conditions to estimate the sparsity, the proposed algorithm realizes accurate reconstruction and estimates the true supporting set of approximated signal. The analytical theory and simulation results show that the SABIHT algorithm recovers effectively the signals without prior information of signal sparsity and the reconstruction performance is similar to the BIHT algorithm.