  This work considers reconstructing a target signal in a context of
distributed sparse sources. We propose an efficient reconstruction algorithm
with the aid of other given sources as multiple side information (SI). The
proposed algorithm takes advantage of compressive sensing (CS) with SI and
adaptive weights by solving a proposed weighted $n$-$\ell_{1}$ minimization.
The proposed algorithm computes the adaptive weights in two levels, first each
individual intra-SI and then inter-SI weights are iteratively updated at every
reconstructed iteration. This two-level optimization leads the proposed
reconstruction algorithm with multiple SI using adaptive weights (RAMSIA) to
robustly exploit the multiple SIs with different qualities. We experimentally
perform our algorithm on generated sparse signals and also correlated feature
histograms as multiview sparse sources from a multiview image database. The
results show that RAMSIA significantly outperforms both classical CS and CS
with single SI, and RAMSIA with higher number of SIs gained more than the one
with smaller number of SIs.
