Noisy 1-Bit Compressed Sensing Recovery Algorithm with Landsberg-Vedral Entropy

在信号、图像及视频恢复领域，二值压缩感知(1-bit compressed sensing, 1BCS)近年来由于其采样和硬件实现上的优势而广受关注。然而，1BCS在应对符号翻转噪声或稀疏度/噪声水平先验信息难以获取等问题上依然具有挑战性。本文提出了基于Landsberg-Vedral熵的鲁棒广义不动点延拓算法(robust generalized fix point continuation, RGFPC)。一方面，RGFPC将不动点延拓(fix point continuation, FPC)系统与探测符号翻转位点的技术结合起来，进而使原始信号可以在没有稀疏度/噪声水平先验时由更新后的测量值被自适应地恢复。另一方面，我们从理论上证明了LV熵在稀疏增强和能量集中上的有效性，并将LV熵引入至我们的框架中，以此提升FPC系统的恢复性能。最后，我们测试了基于LV熵的RGFPC算法在虚拟信号和CT图像恢复上的有效性和优越性。In the field of signal, image, and video reconstruction, 1-bit compressed sensing (1BCS) has garnered significant attention in recent years due to its advantages in sampling and hardware implementation. However, 1BCS still faces challenges when dealing with issues such as sign-flip noise or difficulty in obtaining prior information on sparsity/noise levels. This paper proposes a robust generalized fixed-point continuation algorithm (RGFPC) based on Landsberg-Vedral entropy. On the one hand, RGFPC integrates the fix point continuation (FPC) system with a technique for detecting sign-flip positions, enabling the original signal to be adaptively recovered from the refined and updated measurements without prior knowledge of sparsity/noise levels. On the other hand, we theoretically demonstrate the effectiveness of LV entropy in sparse enhancement and energy concentration, and introduce LV entropy into our framework to improve the performance of the FPC system. Finally, we test the effectiveness and superiority of the RGFPC algorithm based on LV entropy in virtual signal and CT image reconstruction.