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On the design of linear projections for compressive sensing with side information

Chen, M; Renna, Francesco; Rodrigues, Miguel; (2016) On the design of linear projections for compressive sensing with side information. In: 2016 IEEE International Symposium on Information Theory (ISIT). (pp. pp. 670-674). IEEE Green open access

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Abstract

In this paper, we study the problem of projection kernel design for the reconstruction of high-dimensional signals from low-dimensional measurements in the presence of side information, assuming that the signal of interest and the side information signal are described by a joint Gaussian mixture model (GMM). In particular, we consider the case where the projection kernel for the signal of interest is random, whereas the projection kernel associated to the side information is designed. We then derive sufficient conditions on the number of measurements needed to guarantee that the minimum meansquared error (MMSE) tends to zero in the low-noise regime. Our results demonstrate that the use of a designed kernel to capture side information can lead to substantial gains in relation to a random one, in terms of the number of linear projections required for reliable reconstruction.

Type: Proceedings paper
Title: On the design of linear projections for compressive sensing with side information
Event: 2016 IEEE International Symposium on Information Theory (ISIT)
Location: Barcelona, Spain
Dates: 10 July 2016 - 15 July 2016
ISBN-13: 9781509018062
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/ISIT.2016.7541383
Publisher version: http://ieeexplore.ieee.org/document/7541383/
Language: English
Additional information: Copyright © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Keywords: Kernel design, side information, Gaussian mixture model (GMM), minimum mean squared error (MMSE)
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/1530189
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