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 quadratic compressed sensing, 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 efficiently tackle the emerging overdetermined linear feasibility problem, we further propose an enhanced randomized Kaczmarz algorithm, called Block SKM. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.

翻译：具有时变采样阈值的一比特量化因其较低功耗和实现成本，近年来在统计信号处理应用中展现出显著的利用潜力。除上述优势外，一比特模数转换器的一个吸引人特性是其采样率优于传统的多比特转换器。这一特性赋予一比特信号处理框架一种我们称之为“样本充裕”的能力。另一方面，许多信号恢复和优化问题在一比特采样机制下被表述为（可能非凸的）二次规划，并带有线性可行性约束。我们以二次压缩感知为重点，证明样本充裕范式允许通过构建大规模超定线性系统，将此类二次问题转化为单纯的线性可行性问题，从而消除对昂贵优化约束和目标的需求。为高效处理出现的超定线性可行性问题，我们进一步提出一种增强型随机Kaczmarz算法，称为Block SKM。数值结果展示了所提方法的有效性。