  Functional depth is the functional data analysis technique that orders a
functional data set. Unlike the case of data on the real line, defining this
order is non-trivial, and particularly, with functional data, there are a
number of properties that any depth should satisfy. We propose a new depth
which both satisfies the properties required of a functional depth but also one
which can be used in the case where there are a very large number of functional
observations or in the case where the observations are functions of several
continuous variables (such as images, for example). We give theoretical
justification for our choice, and evaluate our proposed depth through
simulation. We finally apply the proposed depth to the problem of yielding a
completely non-parametric deconvolution of Positron Emission Tomography (PET)
data for a very large number of curves across the image, as well as to the
problem of finding a representative subject from a set of PET scans.
