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Unlimited Sampling of Sparse Signals
Name
UnlimitedSamplingofSparseSignalsReport.pdf
Description
Accepted version
Size
942.1 KB
Format
Adobe PDF
Checksum (MD5)
5c420f8bdde2f6eda3172301897691b4
Author(s)
Bhandari, Ayush
Krahmer, Felix
Raskar, Ramesh
Date Issued
April 2018
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Bhandari, Ayush, Krahmer, Felix and Raskar, Ramesh. 2018. "Unlimited Sampling of Sparse Signals."
Version
Author's final manuscript
Abstract
© 2018 IEEE. In a recent paper [1], we introduced the concept of 'Unlimited Sampling'. This unique approach circumvents the clipping or saturation problem in conventional analog-to-digital converters (ADCs) by considering a radically different ADC architecture which resets the input voltage before saturation. Such ADCs, also known as Self-Reset ADCs (SR-ADCs), allow for sensing modulo samples. In analogy to Shannon's sampling theorem, the unlimited sampling theorem proves that a bandlimited signal can be recovered from modulo samples provided that a certain sampling density criterion, that is independent of the ADC threshold, is satisfied. In this way, our result allows for perfect recovery of a bandlimited function whose amplitude exceeds the ADC threshold by orders of magnitude. By capitalizing on this result, in this paper, we consider the inverse problem of recovering a sparse signal from its low-pass filtered version. This problem frequently arises in several areas of science and engineering and in context of signal processing, it is studied in several flavors, namely, sparse or FRI sampling, super-resolution and sparse deconvolution. By considering the SR-ADC architecture, we develop a sampling theory for modulo sampling of lowpass filtered spikes. Our main result consists of a new sparse sampling theorem and an algorithm which stably recovers a K -sparse signal from low-pass, modulo samples. We validate our results using numerical experiments.
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
10.1109/icassp.2018.8462231
