Performance bounds for sparse signal reconstruction with multiple side information [arXiv]

In the context of compressive sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information (SI). To address this problem, we propose a reconstruction algorithm with multiple SI (RAMSI) that solves a general weighted n-ℓ1 norm minimization. The proposed RAMSI algorithm takes advantage of both CS and the n-ℓ1 minimization by adaptively computing optimal weights among SI signals at every reconstructed iteration. In addition, we establish theoretical performance bounds on the number of measurements that are required to successfully reconstruct the original sparse source using RAMSI under arbitrary support SI conditions. The analyses of the established bounds reveal that RAMSI can achieve sharper bounds and significant performance improvements compared to classical CS. We evaluate experimentally the proposed algorithm and the established bounds using synthetic sparse signals as well as correlated feature histograms, extracted from a multiview image database for object recognition. The obtained results show clearly that the proposed RAMSI algorithm outperforms classical CS and CS with single SI in terms of both the theoretical bounds and the practical performance.