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Measurement matrix design for compressive sensing with side information at the encoder

Song, P; Deligiannis, N; Rodrigues, M; De Castro Mota, JF; (2016) Measurement matrix design for compressive sensing with side information at the encoder. In: 2016 IEEE Statistical Signal Processing Workshop (SSP). (pp. pp. 1-5). IEEE Green open access

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Abstract

We study the problem of measurement matrix design for Compressive Sensing (CS) when the encoder has access to side information, a signal analogous to the signal of interest. In particular, we propose to incorporate this extra information into the signal acquisition stage via a new design for the measurement matrix. The goal is to reduce the number of encoding measurements, while still allowing perfect signal reconstruction at the decoder. Then, the reconstruction performance of the resulting CS system is analysed in detail assuming the decoder reconstructs the original signal via Basis Pursuit. Finally, Gaussian width tools are exploited to establish a tight theoretical bound for the number of required measurements. Extensive numerical experiments not only validate our approach, but also demonstrate that our design requires fewer measurements for successful signal reconstruction compared with alternative designs, such as an i.i.d. Gaussian matrix.

Type: Proceedings paper
Title: Measurement matrix design for compressive sensing with side information at the encoder
Event: IEEE Statistical Signal Processing Workshop (SSP)
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/SSP.2016.7551810
Publisher version: http://dx.doi.org/10.1109/SSP.2016.7551810
Language: English
Additional information: © 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: Gaussian processes; compressed sensing; decoding; matrix algebra; signal detection; signal reconstruction; CS system; Gaussian width tool; basis pursuit; compressive sensing; decoder; encoder; encoding measurement; measurement matrix design problem; side information; signal acquisition stage; signal reconstruction; Atmospheric measurements; Decoding; Image reconstruction; Minimization; Optimization; Particle measurements; Sea measurements; Basis Pursuit; Compressive Sensing; measurement matrix design; side information
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/1529224
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