Binary compressive sensing and super-resolution with unknown threshold

Mukherjee, S and Sekuboyina, AK and Seelamantula, CS (2019) Binary compressive sensing and super-resolution with unknown threshold. In: 12th International Conference on Signal Processing and Communications, SPCOM 2018, 16 - 19 July 2018, Bangalore, pp. 65-69.

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Abstract

We consider the problem of binary compressive sensing (CS), where random linear projections of a sparse signal are encoded using threshold-crossing information. The threshold used by the binary encoder for acquisition is unknown to the decoder and is estimated jointly with the signal. We cast the problem of signal reconstruction and threshold estimation as one of learning a hyperplane that separates the sampling vectors corresponding to the +1 and -1 measurements, and develop a reconstruction algorithm that entails iterative minimization of reweighted \ell-1-norm subject to a set of linear constraints that enforce measurement separability. The proposed algorithm leads to a reconstruction performance comparable with that obtained using a popular binary CS algorithm, namely binary iterative hard-thresholding, which assumes that the threshold is set to zero. We consider binary super-resolution as an application, where a signal consisting of point sources needs to be estimated from sign measurements of its blurred version. The proposed algorithm successfully recovers the locations and amplitudes of the point sources, even in the presence of significant blurring.

Item Type:	Conference Paper
Publication:	SPCOM 2018 - 12th International Conference on Signal Processing and Communications
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Compressed sensing; Iterative methods; Optical resolving power, Compressive sensing; Iterative hard thresholding; Linear constraints; Linear projections; Reconstruction algorithms; Super resolution; Threshold estimation; Threshold-crossing, Signal reconstruction
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	08 Aug 2022 05:17
Last Modified:	08 Aug 2022 05:17
URI:	https://eprints.iisc.ac.in/id/eprint/75481

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