Multiple Support Recovery Using Very Few Measurements per Sample

Ramesh, L and Murthy, CR and Tyagi, H (2021) Multiple Support Recovery Using Very Few Measurements per Sample. In: 2021 IEEE International Symposium on Information Theory, ISIT 2021, 12-20 Jul 2021, Melbourne, pp. 1748-1753.

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Abstract

In the problem of multiple support recovery, we are given access to linear measurements of multiple sparse samples in \mathbbRd. These samples can be partitioned into \ell groups, with samples having the same support belonging to the same group. For a given budget of m measurements per sample, the goal is to recover the \ell underlying supports, in the absence of the knowledge of group labels. We study this problem with a focus on the measurement-constrained regime where m is smaller than the support size k of each sample. We design a two-step procedure that estimates the union of the underlying supports first, and then uses a spectral algorithm to estimate the individual supports. Our proposed estimator can recover the supports with m < k measurements per sample, from \tildeO(k⁴\ell⁴/m⁴) samples. Our guarantees hold for a general, generative model assumption on the samples and measurement matrices. © 2021 IEEE.

Item Type:	Conference Paper
Publication:	IEEE International Symposium on Information Theory - Proceedings
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:	Budget control; Information theory, Generative model; Linear measurements; Sparse sample; Spectral algorithm; Support recoveries; Two-step procedure, Recovery
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	03 Dec 2021 08:40
Last Modified:	03 Dec 2021 08:40
URI:	http://eprints.iisc.ac.in/id/eprint/70259

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