Diffusive Compressive Sensing

Document Type : Original Article

Authors

1 Faculty of Advanced Technologies, University of Mohaghegh Ardabili, Namin, Iran.

2 Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran.

Abstract

Proper sampling of the spatio-temporal field induced by a source and its recovery from the limited and discrete samples of the sensor network are two important steps in environmental monitoring of the diffusion thermal field. Sampling by sensor networks has limitations: 1) limitation in the number of sensing nodes, which limits the spatial resolution. 2) battery life of the sensor node, which limits the power consumption and temporal sampling rate. Compressive Sensing (CS) is a traditional method to overcome sampling problems of sensor networks, while an efficient scheme is required to recover the field from the samples. In this paper, Diffusive Compressive Sensing (DCS) is proposed to use Partial Differential Equations (PDE) constraint to model the inherent structure of the spatio-temporal field as side information in the compressive sensing problem. According to the method of estimating the time derivative parameter in the PDE at each moment, the DCS-I and DCS-II methods are presented. Also, to better model the dependence between time frames, Kronecker Diffusive Compressive Sensing (KDCS) is proposed in which the structured sensing matrix designed using the Kronecker product. Simulation results indicate that the proposed KDCS method outperforms existing methods.

Keywords

Main Subjects

References

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Tabriz Journal of Electrical Engineering
Volume 55, Issue 2 - Serial Number 112
October 2025
Pages 300-310

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