Compressed sensing of diffusion fields under heat equation constraint

Reconstructing a diffusion field from spatiotemporal measurements is an important problem in engineering and physics with applications in temperature flow, pollution dispersion, and disease epidemic dynamics. In such applications, sensor networks are used as spatiotemporal sampling devices and a relatively large number of spatiotemporal measurements may be required for accurate source field reconstruction. Consequently, due to limitations on the number of nodes in the sensor networks as well as hardware limitations of each sensor, situations may arise where the available spatiotemporal sampling density does not allow for recovery of field details. In this paper, the above limitation is resolved by means of using compressed sensing (CS). We propose to exploit the intrinsic property of diffusive fields as side information to improve the reconstruction results of classic CS which we call diffusive compressed sensing (DCS). Experimental results demonstrate the effectiveness and usefulness of the proposed method in substantial data savings while producing estimates of higher accuracy, as compared to classic CS-base estimates.