Measurement Bounds for Sparse Signal Reconstruction with Multiple Side Information

Abstract

In the context of compressed sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information. To address this problem, we theoretically study a generic blackweighted n-_1 minimization framework and propose a reconstruction algorithm that leverages multiple side information signals (RAMSI). The proposed RAMSI algorithm computes adaptively optimal weights among the side information signals at every reconstruction iteration. In addition, we establish theoretical bounds on the number of measurements that are required to successfully reconstruct the sparse source by using blackweighted n-_1 minimization. The analysis of the established bounds reveal that blackweighted n-_1 minimization can achieve sharper bounds and significant performance improvements compared to classical CS. We evaluate experimentally the proposed RAMSI 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 algorithm outperforms state-of-the-art algorithms---blackincluding classical CS, _1-_1 minimization, Modified-CS, regularized Modified-CS, and weighted _1 minimization---in terms of both the theoretical bounds and the practical performance.

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