Improved Bounds for Universal One-bit Compressive Sensing

Acharya, Jayadev and Bhattacharyya, Arnah and Kamath, Pritish (2017) Improved Bounds for Universal One-bit Compressive Sensing. In: IEEE International Symposium on Information Theory (ISIT), JUN 25-30, 2017, Aachen, GERMANY, pp. 2353-2357.

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Abstract

Unlike compressive sensing where the measurement outputs are assumed to be real-valued and have infinite precision, in one-bit compressive sensing, measurements are quantized to one hit, their signs. In this work, our contributions are as follows: 1. We show how to recover the support of sparse high dimensional vectors in the 1-bit compressive sensing framework with an asymptotically near-optimal number of measurements. We do this by showing an equivalence between the task of support recovery using 1-bit compressive sensing and a well studied combinatorial object known as Union Free Families. 2. We also improve the bounds on the number of measurements for approximately recovering vectors from 1-bit compressive sensing measurements. All our results are about universal measurements, namely the measurement schemes that work simultaneously for all sparse vectors. Our improved bounds naturally lead the way to suggest several interesting open problems.

Item Type:	Conference Proceedings
Series.:	IEEE International Symposium on Information Theory
Publisher:	IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
Additional Information:	Copy right for this article belong to IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	18 May 2018 15:59
Last Modified:	06 Oct 2018 12:48
URI:	http://eprints.iisc.ac.in/id/eprint/59903

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