Approximate message passing for sparse recovering of spatially and temporally correlated data

To meet the need of data-intensive continuous monitoring, recent research on energy-efficient data gathering in wireless sensor networks (WSNs) has explored the use of compressive sensing (CS) to exploit both spatial and temporal correlations in data. However, the performance of CS-based data gathering methods has been limited since most work only considers the structured sparsity of natural signals and ignores the amplitude correlations of the signals. In this paper, the structured sparsity and the amplitude correlations are considered jointly by assuming the spatially and temporally correlated data satisfies simultaneous low-rank and joint-sparse (L&S) structure. Using a structured L&S factorization, we then propose an iterative approximate message passing (AMP) algorithm for joint CS reconstruction of the data, where the low-rankness and sparsity pattern decoding phase is formulated as a variant of the principal component analysis (PCA) problem and employs the bilinear generalized approximate message passing algorithm (BiG-AMP) to perform denoising effectively. In addition, a rank selection strategy and an expectation-maximization (EM) estimation strategy that adaptively tune model parameters are described. Simulation results with synthetic and real data suggest that the proposed algorithm outperforms the state-of-the-art reconstruction algorithms with substantial reduction in complexity.