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arXiv 2309.04045cs.ITmath.IT
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带抖动一位量化的低秩矩阵感知

Low-rank Matrix Sensing With Dithered One-Bit Quantization

Farhang Yeganegi, Arian Eamaz, Mojtaba Soltanalian

AI总结:

该研究针对抖动一位采样的极端场景,提出改进的随机Kaczmarz算法从高度量化数据中恢复低秩矩阵,给出收敛性与样本量理论保证,数值实验验证了方法有效性。

摘要:

我们在抖动一位采样的极端场景下探究粗量化对低秩矩阵感知的影响,该场景中高分辨率测量值会与随时间变化的随机阈值进行比较。为从高度量化的采集数据中恢复目标低秩矩阵,我们提出了一种改进的随机Kaczmarz算法,可高效求解由此产生的超定可行性问题。此外,我们还给出了收敛性和样本量要求方面的理论保证。数值结果验证了所提方法的有效性。

英文摘要:

We explore the impact of coarse quantization on low-rank matrix sensing in the extreme scenario of dithered one-bit sampling, where the high-resolution measurements are compared with random time-varying threshold levels. To recover the low-rank matrix of interest from the highly-quantized collected data, we offer an enhanced randomized Kaczmarz algorithm that efficiently solves the emerging highly-overdetermined feasibility problem. Additionally, we provide theoretical guarantees in terms of the convergence and sample size requirements. Our numerical results demonstrate the effectiveness of the proposed methodology.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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