One-Bit Matrix Completion With Time-Varying Sampling Thresholds

Arian Eamaz, Farhang Yeganegi, Mojtaba Soltanalian

Abstract:

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.

Submission Type: Full Paper