Seminar Details
2021-03-23 (14h) : Computational Sensing via Signal Folding: Variations on a Theme
At MS Teams
Organized by Mathematical Engineering
Speaker :
Ayush Bhandari (Imperial College London, UK)
Abstract :
Digital 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 the Unlimited Sensing framework or the 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 followed by certain variations on the theme. We show that, remarkably, 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. We then discuss sampling of sparse and parametric signals. Beyond the theoretical results, we will also present a hardware demo that shows our approach in action.
Moving further, we reinterpret the unlimited sensing framework 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.