Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral estimation on a sphere in geophysics and cosmology   We address the problem of estimating the spherical-harmonic power spectrum of
a statistically isotropic scalar signal from noise-contaminated data on a
region of the unit sphere. Three different methods of spectral estimation are
considered: (i) the spherical analogue of the one-dimensional (1-D)
periodogram, (ii) the maximum likelihood method, and (iii) a spherical analogue
of the 1-D multitaper method. The periodogram exhibits strong spectral leakage,
especially for small regions of area $A\ll 4\pi$, and is generally unsuitable
for spherical spectral analysis applications, just as it is in 1-D. The maximum
likelihood method is particularly useful in the case of nearly-whole-sphere
coverage, $A\approx 4\pi$, and has been widely used in cosmology to estimate
the spectrum of the cosmic microwave background radiation from spacecraft
observations. The spherical multitaper method affords easy control over the
fundamental trade-off between spectral resolution and variance, and is easily
implemented regardless of the region size, requiring neither non-linear
iteration nor large-scale matrix inversion. As a result, the method is ideally
suited for most applications in geophysics, geodesy or planetary science, where
the objective is to obtain a spatially localized estimate of the spectrum of a
signal from noisy data within a pre-selected and typically small region.

27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
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The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an