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.

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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.

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