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The use of side information in Compressive Sensing: Measurement design and signal reconstruction

Song, P; De Castro Mota, J; Deligiannis, N; Rodrigues, M; (2016) The use of side information in Compressive Sensing: Measurement design and signal reconstruction. In: Proceedings of the 11th IMA International Conference on Mathematics in Signal Processing. Institute of Mathematics and its Applications: Birmingham, UK. Green open access

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Abstract

We study the problem of sparse signal acquisition and reconstruction known as Compressive Sensing (CS) in the presence of side information, i.e., a class of signals correlated with the target signal. Side-information aided CS has been applied in various fields, such as medical imaging, remote sensing, sensor networks and compressive video. In this context, we consider a setup where the side information is available during both the signal acquisition stage, at the encoder, and the signal reconstruction stage, at the decoder. Our approach leverages side information to construct specific measurement matrices and then integrates side information into signal reconstruction by solving a ℓ1-ℓ1 minimization problem. The exploitation of side information both at the encoder and decoder allows us to achieve successful signal reconstruction with fewer measurements than just using side information at the decoder. This is shown theoretically, via establishing bounds on the number of measurements, as well as experimentally, via a series of simulations.

Type: Proceedings paper
Title: The use of side information in Compressive Sensing: Measurement design and signal reconstruction
Event: 11th IMA International Conference on Mathematics in Signal Processing
Location: IET Austin Court, Birmingham, UK
Dates: 12 December 2016 - 14 December 2016
Open access status: An open access version is available from UCL Discovery
Publisher version: https://ima.org.uk/proceedings/
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Compressive Sensing, side information, measurement matrix, ℓ1-ℓ1 minimization
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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/1530197
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