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Compressive Sensing With Side Information: How to Optimally Capture This Extra Information for GMM Signals?

Chen, M; Renna, F; Rodrigues, MRD; (2018) Compressive Sensing With Side Information: How to Optimally Capture This Extra Information for GMM Signals? IEEE Transactions on Signal Processing , 66 (9) pp. 2314-2329. 10.1109/TSP.2018.2807411. Green open access

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Abstract

This paper studies how to optimally capture side information to aid in the reconstruction of high-dimensional signals from low-dimensional random linear and noisy measurements, by assuming that both the signal of interest and the side information signal are drawn from a joint Gaussian mixture model. In particular, we derive sufficient and (occasionally) necessary conditions on the number of linear measurements for the signal reconstruction minimum mean squared error (MMSE) to approach zero in the low-noise regime; moreover, we also derive closed-form linear side information measurement designs for the reconstruction MMSE to approach zero in the low-noise regime. Our designs suggest that a linear projection kernel that optimally captures side information is such that it measures the attributes of side information that are maximally correlated with the signal of interest. A number of experiments both with synthetic and real data confirm that our theoretical results are well aligned with numerical ones. Finally, we offer a case study associated with a panchromatic sharpening (pan sharpening) application in the presence of compressive hyperspectral data that demonstrates that our proposed linear side information measurement designs can lead to reconstruction peak signal-to-noise ratio (PSNR) gains in excess of 2 dB over other approaches in this practical application.

Type: Article
Title: Compressive Sensing With Side Information: How to Optimally Capture This Extra Information for GMM Signals?
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TSP.2018.2807411
Publisher version: https://doi.org/10.1109/TSP.2018.2807411
Language: English
Additional information: © 2018 IEEE. This work is licensed under a Creative Commons Attribution 3.0 License (http://creativecommons.org/licenses/by/3.0/).
Keywords: compressive sensing, compressive sensing with side information, random projection kernels, linear projection kernel design, Gaussian mixture models (GMM), pan-sharpening
UCL classification: 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: http://discovery.ucl.ac.uk/id/eprint/10051933
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