Sparse Signal Reconstruction with Multiple Side Information using Adaptive Weights for Multiview Sources

This work considers reconstructing a target signal in a context ofdistributed sparse sources. We propose an efficient reconstruction algorithmwith the aid of other given sources as multiple side information (SI). Theproposed algorithm takes advantage of compressive sensing (CS) with SI andadaptive weights by solving a proposed weighted $n$-$\ell_{1}$ minimization.The proposed algorithm computes the adaptive weights in two levels, first eachindividual intra-SI and then inter-SI weights are iteratively updated at everyreconstructed iteration. This two-level optimization leads the proposedreconstruction algorithm with multiple SI using adaptive weights (RAMSIA) torobustly exploit the multiple SIs with different qualities. We experimentallyperform our algorithm on generated sparse signals and also correlated featurehistograms as multiview sparse sources from a multiview image database. Theresults show that RAMSIA significantly outperforms both classical CS and CSwith single SI, and RAMSIA with higher number of SIs gained more than the onewith smaller number of SIs.