On Unlimited Sampling and Reconstruction
On Unlimited Sampling and Reconstruction
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DOI：
10.1109/tsp.2020.3041955
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发表时间：
2019-05
影响因子：
5.4
通讯作者：
Ayush Bhandari;F. Krahmer;R. Raskar
中科院分区：
文献类型：
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作者：
Ayush Bhandari;F. Krahmer;R. Raskar
香农的采样定理，在数字信号处理的核心，是很好的理解和探索。然而，由于底层模数转换器（adc）的动态范围限制，其实际实现仍然受到基本瓶颈的影响。这将导致信号幅度超过其最大可记录电压的削波或饱和，从而导致显著的信息损失。在本文中，我们开发了一种用于感知和恢复的替代范例，称为无限采样框架。关键的观察结果是，在ADC之前对信号进行模操作可以防止饱和；相反，人们会遇到另一种类型的信息丢失。这样的设置可以实现，例如，通过所谓的折叠或自复位adc，在电路设计文献的各种背景下提出。这种新型信息丢失的关键挑战是从其模采样中恢复带限信号。给出了完全恢复的条件，并给出了稳定恢复算法。所需的采样密度与最大可记录ADC电压无关，仅取决于信号带宽。我们的保证扩展到受有界噪声影响的测量，其中包括四舍五入量化。数值实验验证了我们的方法。例如，从量化模采样到不可避免的量化误差，可以恢复幅度高于ADC阈值的函数。无限采样范式的应用可以在信号处理、通信和成像等许多领域找到。
Shannon's sampling theorem, at the heart of digital signal processing, is well understood and explored. However, its practical realization still suffers from a fundamental bottleneck due to dynamic range limitations of the underlying analog–to–digital converters (ADCs). This results in clipping or saturation for signal amplitudes exceeding their maximum recordable voltage thus leading to a significant information loss. In this paper, we develop an alternative paradigm for sensing and recovery, called the Unlimited Sampling Framework. The key observation is that applying a modulo operation to the signal before the ADC prevents saturation; instead, one encounters a different type of information loss. Such a setup can be implemented, for example, via so-called folding or self-reset ADCs, as proposed in various contexts in the circuit design literature. The key challenge for this new type of information loss is to recover a bandlimited signal from its modulo samples. We derive conditions when perfect recovery is possible and complement them with a stable recovery algorithm. The required sampling density is independent of the maximum recordable ADC voltage and depends on the signal bandwidth only. Our guarantees extend to measurements affected by bounded noise, which includes round-off quantization. Numerical experiments validate our approach. For example, it is possible to recover functions with amplitudes orders of magnitude higher than the ADC's threshold from quantized modulo samples up to the unavoidable quantization error. Applications of the unlimited sampling paradigm can be found in a number of fields such as signal processing, communication and imaging.