Reconstructive Mapping from Sparsely-Sampled Groundwater Data Using Compressive Sensing

Abstract

Compressive sensing is a powerful method for reconstruction of sparsely-sampled data, based on statistical optimization. It can be applied to a range of flow measurement and visualization data, and in this work we show the usage in groundwater mapping. Due to scarcity of water in many regions of the world, including southwestern United States, monitoring and management of groundwater is of utmost importance. A complete mapping of groundwater is difficult since the monitored sites are far from one another, and thus the data sets are considered extremely “sparse”. To overcome this difficulty in complete mapping of groundwater, compressive sensing is an ideal tool, as it bypasses the classical Nyquist criterion. We show that compressive sensing can effectively be used for reconstructions of groundwater level maps, by validating against data. This approach can have an impact on geographical sensing and information, as effective monitoring and management are enabled without constructing numerous or expensive measurement sites for groundwater.