  The motion of and interaction between phase singularities that anchor spiral
waves captures many qualitative and, in some cases, quantitative features of
complex dynamics in excitable systems. Being able to accurately reconstruct
their position is thus quite important, even if the data are noisy and sparse,
as in electrophysiology studies of cardiac arrhythmias, for instance. A
recently proposed global topological approach [Marcotte & Grigoriev, Chaos 27,
093936 (2017)] promises to dramatically improve the quality of the
reconstruction compared with traditional, local approaches. Indeed, we found
that this approach is capable of handling noise levels exceeding the range of
the signal with minimal loss of accuracy. Moreover, it also works successfully
with data sampled on sparse grids with spacing comparable to the mean
separation between the phase singularities for complex patterns featuring
multiple interacting spiral waves.
