  Large-scale data collection by means of wireless sensor network and
internet-of-things technology poses various challenges in view of the
limitations in transmission, computation, and energy resources of the
associated wireless devices. Compressive data gathering based on compressed
sensing has been proven a well-suited solution to the problem. Existing designs
exploit the spatiotemporal correlations among data collected by a specific
sensing modality. However, many applications, such as environmental monitoring,
involve collecting heterogeneous data that are intrinsically correlated. In
this study, we propose to leverage the correlation from multiple heterogeneous
signals when recovering the data from compressive measurements. To this end, we
propose a novel recovery algorithm---built upon belief-propagation
principles---that leverages correlated information from multiple heterogeneous
signals. To efficiently capture the statistical dependencies among diverse
sensor data, the proposed algorithm uses the statistical model of copula
functions. Experiments with heterogeneous air-pollution sensor measurements
show that the proposed design provides significant performance improvements
against state-of-the-art compressive data gathering and recovery schemes that
use classical compressed sensing, compressed sensing with side information, and
distributed compressed sensing.
