  Wavelets are widely used in various disciplines to analyse signals both in
space and scale. Whilst many fields measure data on manifolds (i.e., the
sphere), often data are only observed on a partial region of the manifold.
Wavelets are a typical approach to data of this form, but the wavelet
coefficients that overlap with the boundary become contaminated and must be
removed for accurate analysis. Another approach is to estimate the region of
missing data and to use existing whole-manifold methods for analysis. However,
both approaches introduce uncertainty into any analysis. Slepian wavelets
enable one to work directly with only the data present, thus avoiding the
problems discussed above. Applications of Slepian wavelets to areas of research
measuring data on the partial sphere include gravitational/magnetic fields in
geodesy, ground-based measurements in astronomy, measurements of whole-planet
properties in planetary science, geomagnetism of the Earth, and cosmic
microwave background analyses.
