"Sampling via Modulo Folding: Revisiting the Legacy of Shannon-Nyquist, Prony, Schoenberg, Pisarenko and Radon"Bhandari, AyushDigital data capture is the backbone of all modern day systems and “Digital Revolution” has been aptly termed as the Third Industrial Revolution. Underpinning the digital representation is the Shannon-Nyquist sampling theorem and more recent developments such as compressive sensing approaches. The fact that there is a physical limit to which sensors can measure amplitudes poses a fundamental bottleneck when it comes to leveraging the performance guaranteed by recovery algorithms. In practice, whenever a physical signal exceeds the maximum recordable range, the sensor saturates, resulting in permanent information loss. Examples include (a) dosimeter saturation during the Chernobyl reactor accident, reporting radiation levels far lower than the true value, and (b) loss of visual cues in self-driving cars coming out of a tunnel (due to sudden exposure to light). To reconcile this gap between theory and practice, we introduce a computational sensing approach—the Unlimited Sensing framework (USF)—that is based on a co-design of hardware and algorithms. On the hardware front, our work is based on a radically different analog-to-digital converter (ADC) design, which allows for the ADCs to produce modulo or folded samples. On the algorithms front, we develop new, mathematically guaranteed recovery strategies. In the first part of this talk, we prove a sampling theorem akin to the Shannon-Nyquist criterion. Despite the non-linearity in the sensing pipeline, the sampling rate only depends on the signal’s bandwidth. Our theory is complemented with a stable recovery algorithm. Beyond the theoretical results, we also present a hardware demo that shows the modulo ADC in action. Building on the basic sampling theory result, we consider certain variations on the theme. This includes different signal classes (e.g. smooth, sparse and parametric functions) as well as sampling architectures, such as One-Bit and Event-Triggered sampling. Moving further, we reinterpret the USF as a generalized linear model that motivates a new class of inverse problems. We conclude this talk by presenting a research overview in the context of single-shot high-dynamic-range (HDR) imaging, sensor array processing and HDR computed tomography based on the modulo Radon transform. |
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