  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.
