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One-bit quantization with time-varying sampling thresholds has recently foundsignificant utilization potential in statistical signal processing applicationsdue to its relatively low power consumption and low implementation cost. Inaddition to such advantages, an attractive feature of one-bit analog-to-digitalconverters (ADCs) is their superior sampling rates as compared to theirconventional multi-bit counterparts. This characteristic endows one-bit signalprocessing frameworks with what we refer to as sample abundance. On the otherhand, many signal recovery and optimization problems are formulated as(possibly non-convex) quadratic programs with linear feasibility constraints inthe one-bit sampling regime. We demonstrate, with a particular focus on thenuclear norm minimization, that the sample abundance paradigm allows for thetransformation of such quadratic problems to merely a linear feasibilityproblem by forming a large-scale overdetermined linear system; thus removingthe need for costly optimization constraints and objectives. To make thisachievable, we propose enhanced randomized Kaczmarz algorithms to tackle thesehighly overdetermined feasibility problems. Several numerical results arepresented to illustrate the effectiveness of the proposed methodologies.

ORKA: Accelerated Kaczmarz Algorithms for Signal Recovery from One-Bit Samples