Signal Processing Seminar

On Unlimited Sampling and Reconstruction: A New Way to Sense the Continuum

Ayush Bhandari

Almost all forms of data are captured using digital sensors or analog-to-digital converters (ADCs) which are inherently limited by dynamic range. Consequently, whenever a physical signal exceeds the maximum recordable voltage, the digital sensor saturates and results in clipped measurements. For example, a camera pointed towards the sun leads to an all-white photograph. Motivated by a variety of applications including scientific imaging, communication theory and digital sensing, a natural question that arises is: Can we capture a signal with arbitrary dynamic range?

In this work, we introduce the Unlimited Sensing framework which is a novel, non-linear sensing architecture that allows for recovery of an arbitrarily high dynamic range, continuous-time signal from its low dynamic range, digital measurements. Our work is based on a radically different ADC design, which allows for the ADC to reset rather than to saturate, thus producing modulo or folded samples.

In the first part of this talk, we discuss a recovery guarantee akin to Shannon’s sampling theorem which, remarkably, is independent of the maximum recordable ADC voltage. Our theory is complemented with a stable recovery algorithm. Moving further, we reinterpret the unlimited sensing framework as a generalized linear model and discuss the recovery of structured signals such as continuous-time sparse signals. This new sensing paradigm that is based on a co-design of hardware and algorithms leads to several interesting future research directions. On the theoretical front, a fundamental interplay of sampling theory and inverse problems raises new standalone questions. On the practical front, the benefits of a new way to sense the world (without dynamic range limitations) are clearly visible. We conclude this talk with a discussion on future directions and relevant applications.

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Overview of Signal Processing Seminar