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Measurement matrix design for compressive sensing with side information at the encoder Host Publication: 2016 IEEE Workshop on Statistical Signal Processing (SSP 2016) Authors: P. Song, J. Mota, N. Deligiannis and M. Rodrigues Publisher: IEEE Publication Year: 2016 Number of Pages: 5 ISBN: 978-1-4673-7804-8
Abstract: We study the problem of measurement matrix design for Com- pressive Sensing (CS) when the encoder has access to side infor- mation, a signal analogous to the signal of interest. In particular, we propose to incorporate this extra information into the signal ac- quisition 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 re- construction performance of the resulting CS system is analysed in detail assuming the decoder reconstructs the original signal via Ba- sis 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.
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