Graph Signal Reconstruction Techniques for IoT Air Pollution Monitoring Platforms

Air pollution monitoring platforms play a very important role in preventing and mitigating the effects of pollution. Recent advances in the field of graph signal processing have made it possible to describe and analyze air pollution monitoring networks using graphs. One of the main applications is the reconstruction of the measured signal in a graph using a subset of sensors. Reconstructing the signal using information from sensor neighbors can help improve the quality of network data, examples are filling in missing data with correlated neighboring nodes, or correcting a drifting sensor with neighboring sensors that are more accurate. This paper compares the use of various types of graph signal reconstruction methods applied to real data sets of Spanish air pollution reference stations. The methods considered are Laplacian interpolation, graph signal processing low-pass based graph signal reconstruction, and kernel-based graph signal reconstruction, and are compared on actual air pollution data sets measuring O3, NO2, and PM10. The ability of the methods to reconstruct the signal of a pollutant is shown, as well as the computational cost of this reconstruction. The results indicate the superiority of methods based on kernel-based graph signal reconstruction, as well as the difficulties of the methods to scale in an air pollution monitoring network with a large number of low-cost sensors. However, we show that scalability can be overcome with simple methods, such as partitioning the network using a clustering algorithm.