Multi-Mobile Sensing With Temporal-Spatial Coupling via Compressed Sensing

In this paper, the problem of using a limited number of mobile sensors to sense/measure a time-varying distribution of a field over a multi dimensional space is considered. As the number of sensors, in general, is not adequate for capturing the dynamic distribution with the needed spatial resolution, the sensors are required to be transited between the sampled locations, resulting in intermittent measurement at each sampled location. Therefore, it becomes challenging to use the measured data to recover/restore not only the dynamic process at each sampled/measured location, but also the dynamic distribution over the entire measured space, with high temporal and spatial resolutions. Such a multi-mobile sensing problem, however, cannot be addressed by using existing methods directly. In this work, we propose to tackle this problem through the compressed sensing framework. The randomness requirement of the compressed sensing, however, results in the temporal-spatial coupling, and the constraints in selecting the sampled locations due to the limit of the sensor speed. We propose a spatial-temporal pairing method to avoid the temporal-spatial coupling, and a checking-and-removal process to remove the sensor speed constraint. Simulation results of a video recovery example is presented and discussed to illustrate the proposed method.