Numerous physical phenomena are well modeled by partial
differential equations (PDEs); they describe a wide range of
phenomena across many application domains, from model-
ing EEG signals in electroencephalography to, modeling the
release and propagation of toxic substances in environmental
monitoring. In these applications it is often of interest to find
the sources of the resulting phenomena, given some sparse
sensor measurements of it. This will be the main task of this
work. Specifically, we will show that finding the sources of
such PDE-driven fields can be turned into solving a class of
well-known multi-dimensional structured least squares prob-
lems. This link is achieved by leveraging from recent results
in modern sampling theory – in particular, the approximate
Strang-Fix theory. Subsequently, numerical simulation re-
sults are provided in order to demonstrate the validity and
robustness of the proposed framework.