基于单比特抖动样本的矩阵补全
Matrix Completion from One-Bit Dither Samples
AI总结：
研究抖动单比特感知下的矩阵补全问题，提出OB-SVT算法及三种加速变体，利用时变阈值和草图数据显著提升了低秩矩阵的恢复性能。
摘要：
我们探讨了粗量化在抖动单比特感知这一极端场景下对矩阵补全的影响，其中矩阵元素与随时间变化的阈值水平进行比较。具体而言，我们不再观测低秩矩阵的高分辨率元素子集，而是获取少量由这些比较产生的单比特样本。为了利用粗量化的已知元素恢复低秩矩阵，我们首先将具有时变阈值的单比特矩阵补全（one-bit MC）问题转化为核范数最小化问题。单比特采样信息被表示为线性不等式可行性约束。随后，我们改进了流行的奇异值阈值（SVT）算法以适应这些不等式约束，从而创建了单比特SVT（OB-SVT）。我们的研究结果表明，在单比特MC中引入多个时变采样阈值序列能显著提升矩阵补全算法的性能。为实现该目标，我们采用了多种阈值方案，即均匀、高斯和离散阈值。为加速所提算法的收敛，我们引入了OB-SVT算法的三种变体。其中一种变体是随机化草图OB-SVT，它不再每次迭代使用全部信息，而是选择利用草图数据。该方法有效降低了运算空间的维度并加速了收敛。我们进行了数值评估，将所提算法与先前用于单比特MC的最大似然估计方法进行比较，结果表明我们的方法能够实现更好的恢复性能。
英文摘要：
We explore the impact of coarse quantization on matrix completion in the extreme scenario of dithered one-bit sensing, where the matrix entries are compared with time-varying threshold levels. In particular, instead of observing a subset of high-resolution entries of a low-rank matrix, we have access to a small number of one-bit samples, generated as a result of these comparisons. In order to recover the low-rank matrix using its coarsely quantized known entries, we begin by transforming the problem of one-bit matrix completion (one-bit MC) with time-varying thresholds into a nuclear norm minimization problem. The one-bit sampled information is represented as linear inequality feasibility constraints. We then develop the popular singular value thresholding (SVT) algorithm to accommodate these inequality constraints, resulting in the creation of the One-Bit SVT (OB-SVT). Our findings demonstrate that incorporating multiple time-varying sampling threshold sequences in one-bit MC can significantly improve the performance of the matrix completion algorithm. In pursuit of achieving this objective, we utilize diverse thresholding schemes, namely uniform, Gaussian, and discrete thresholds. To accelerate the convergence of our proposed algorithm, we introduce three variants of the OB-SVT algorithm. Among these variants is the randomized sketched OB-SVT, which departs from using the entire information at each iteration, opting instead to utilize sketched data. This approach effectively reduces the dimension of the operational space and accelerates the convergence. We perform numerical evaluations comparing our proposed algorithm with the maximum likelihood estimation method previously employed for one-bit MC, and demonstrate that our approach can achieve a better recovery performance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
