Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A spatiospectral localization approach to estimating potential fields on
  the surface of a sphere from noisy, incomplete data taken at satellite
  altitudes   Satellites mapping the spatial variations of the gravitational or magnetic
fields of the Earth or other planets ideally fly on polar orbits, uniformly
covering the entire globe. Thus, potential fields on the sphere are usually
expressed in spherical harmonics, basis functions with global support. For
various reasons, however, inclined orbits are favorable. These leave a "polar
gap": an antipodal pair of axisymmetric polar caps without any data coverage,
typically smaller than 10 degrees in diameter for terrestrial gravitational
problems, but 20 degrees or more in some planetary magnetic configurations. The
estimation of spherical harmonic field coefficients from an incompletely
sampled sphere is prone to error, since the spherical harmonics are not
orthogonal over the partial domain of the cut sphere. Although approaches based
on wavelets have gained in popularity in the last decade, we present a method
for localized spherical analysis that is firmly rooted in spherical harmonics.
We construct a basis of bandlimited spherical functions that have the majority
of their energy concentrated in a subdomain of the unit sphere by solving
Slepian's (1960) concentration problem in spherical geometry, and use them for
the geodetic problem at hand. Most of this work has been published by us
elsewhere. Here, we highlight the connection of the "spherical Slepian basis"
to wavelets by showing their asymptotic self-similarity, and focus on the
computational considerations of calculating concentrated basis functions on
irregularly shaped domains.

25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph