  One-bit quantization with time-varying sampling thresholds has recently found
significant utilization potential in statistical signal processing applications
due to its relatively low power consumption and low implementation cost. In
addition to such advantages, an attractive feature of one-bit analog-to-digital
converters (ADCs) is their superior sampling rates as compared to their
conventional multi-bit counterparts. This characteristic endows one-bit signal
processing frameworks with what we refer to as sample abundance. On the other
hand, many signal recovery and optimization problems are formulated as
(possibly non-convex) quadratic programs with linear feasibility constraints in
the one-bit sampling regime. We demonstrate, with a particular focus on the
nuclear norm minimization, that the sample abundance paradigm allows for the
transformation of such quadratic problems to merely a linear feasibility
problem by forming a large-scale overdetermined linear system; thus removing
the need for costly optimization constraints and objectives. To make this
achievable, we propose enhanced randomized Kaczmarz algorithms to tackle these
highly overdetermined feasibility problems. Several numerical results are
presented to illustrate the effectiveness of the proposed methodologies.
