We explore the impact of coarse quantization on low-rank matrix sensing in the extreme scenario of dithered one-bit sampling, where the high-resolution measurements are compared with random time-varying threshold levels. To recover the low-rank matrix of interest from the highly-quantized collected data, we offer an enhanced randomized Kaczmarz algorithm that efficiently solves the emerging highly-overdetermined feasibility problem. Additionally, we provide theoretical guarantees in terms of the convergence and sample size requirements. Our numerical results demonstrate the effectiveness of the proposed methodology.

翻译：我们研究了粗量化对低秩矩阵感知的影响，并聚焦于抖动一位量化的极端场景，其中高分辨率测量值与随机时变阈值电平进行比较。为了从高度量化的收集数据中恢复目标低秩矩阵，我们提出了一种增强型随机Kaczmarz算法，该算法能够高效求解新出现的高度超定可行性问题。此外，我们提供了关于收敛性和样本量需求的理论保证。数值结果验证了所提方法的有效性。