THRESHOLDING-BASED RECONSTRUCTION OF COMPRESSED CORRELATED SIGNALS

We consider the problem of recovering a set of correlated signals (e.g., images from different viewpoints) from a few linear measure-ments per signal. We assume that each sensor in a network acquires a compressed signal in the form of linear measurements and sends it to a joint decoder for reconstruction. We propose a novel joint reconstruction algorithm that exploits correlation among underlying signals. Our correlation model considers geometrical transforma-tions between the supports of the different signals. The proposed joint decoder estimates the correlation and reconstructs the signals using a simple thresholding algorithm. We give both theoretical and experimental evidence to show that our method largely outperforms independent decoding in terms of support recovery and reconstruc-tion quality