  The Interstellar Boundary Explorer (IBEX) satellite has been in orbit since
2008 and detects energy-resolved energetic neutral atoms (ENAs) originating
from the heliosphere. Different regions of the heliosphere generate ENAs at
different rates. It is of scientific interest to take the data collected by
IBEX and estimate spatial maps of heliospheric ENA rates (referred to as sky
maps) at higher resolutions than before. These sky maps will subsequently be
used to discern between competing theories of heliosphere properties that are
not currently possible. The data IBEX collects present challenges to sky map
estimation. The two primary challenges are noisy and irregularly spaced data
collection and the IBEX instrumentation's point spread function. In essence,
the data collected by IBEX are both noisy and biased for the underlying sky map
of inferential interest. In this paper, we present a two-stage sky map
estimation procedure called Theseus. In Stage 1, Theseus estimates a blurred
sky map from the noisy and irregularly spaced data using an ensemble approach
that leverages projection pursuit regression and generalized additive models.
In Stage 2, Theseus deblurs the sky map by deconvolving the PSF with the
blurred map using regularization. Unblurred sky map uncertainties are computed
via bootstrapping. We compare Theseus to a method closely related to the one
operationally used today by the IBEX Science Operation Center (ISOC) on both
simulated and real data. Theseus outperforms ISOC in nearly every considered
metric on simulated data, indicating that Theseus is an improvement over the
current state of the art.
