One-Bit Matrix Completion With Time-Varying Sampling Thresholds

We explore the impact of coarse quantization on matrix completion in the extreme scenario of generalized one-bit sampling, 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. To recover the low-rank matrix from its highly-quantized known entries, we first formulate the one-bit matrix completion problem with time-varying thresholds as a nuclear norm minimization problem, with one-bit sampled information manifested as linear inequality feasibility constraints. We then modify 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 matrix completion can significantly improve the performance of the matrix completion algorithm. We perform numerical evaluations comparing our proposed algorithm with the maximum likelihood estimation method previously employed for one-bit matrix completion, and demonstrate that our approach can achieve a better recovery performance.