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In the context of compressed sensing (CS), this paper considers the problemof reconstructing sparse signals with the aid of other given correlated sourcesas multiple side information. To address this problem, we theoretically study ageneric \textcolor{black}{weighted $n$-$\ell_{1}$ minimization} framework andpropose a reconstruction algorithm that leverages multiple side informationsignals (RAMSI). The proposed RAMSI algorithm computes adaptively optimalweights among the side information signals at every reconstruction iteration.In addition, we establish theoretical bounds on the number of measurements thatare required to successfully reconstruct the sparse source by using\textcolor{black}{weighted $n$-$\ell_{1}$ minimization}. The analysis of theestablished bounds reveal that \textcolor{black}{weighted $n$-$\ell_{1}$minimization} can achieve sharper bounds and significant performanceimprovements compared to classical CS. We evaluate experimentally the proposedRAMSI algorithm and the established bounds using synthetic sparse signals aswell as correlated feature histograms, extracted from a multiview imagedatabase for object recognition. The obtained results show clearly that theproposed algorithm outperforms state-of-the-artalgorithms---\textcolor{black}{including classical CS, $\ell_1\text{-}\ell_1$minimization, Modified-CS, regularized Modified-CS, and weighted $\ell_1$minimization}---in terms of both the theoretical bounds and the practicalperformance.

Measurement Bounds for Sparse Signal Reconstruction with Multiple Side Information