The PIs develop and test the theory and algorithms for a new sampling and reconstruction framework that combines spatial samples of an initial state together with the early time samples of an evolving state to reconstruct the initial distribution and the possibly unknown evolution operator. Using the evolutionary nature of a signal, the PIs aim to recover an initial distribution at a fine resolution from multiple coarse snapshots obtained at appropriate time intervals.
One of the most important aspects of the proposed research is to provide the means to detect potential threats to society (such as chemical, nuclear or biological hazards) using a network of distributed sensors such as the smartphones people carry, rapidly gather and process the information about the threats source location and its distribution and evolution in time, and generate alerts so that appropriate measures are taken to safeguard life and infrastructure. The same ideas can be used in other industrial or biomedical applications in which the time-dependency between samples permits reduction in the number of expensive instruments via the increase of their usage frequency.
