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Summary: ITERATIVE EXTRAPOLATION ALGORITHM FOR DATA RECONSTRUCTION OVER
SPHERE
Wen Zhang, Rodney A. Kennedy and Thushara D. Abhayapala
Department of Information Engineering
Research School of Information Sciences and Engineering
The Australian National University
Email: wen@cecs.anu.edu.au, rodney.kennedy@anu.edu.au, thushara.abhayapala@anu.edu.au
ABSTRACT
Given limited or incomplete measurement data on a sphere, a
new iterative algorithm is proposed on how to extrapolate signal
over the whole sphere. The algorithm is based on a priori assump-
tion that the Fourier decomposition of the signal on the sphere has
finite degree of spherical harmonic coefficients, that is, the signal
is modelimited. The algorithm is a simple iteration involving only
the spherical harmonic decomposition. It is proven that the algo-
rithm converges to the original signal over observation region and
the convergence rate is lower bounded by the largest eigenvalue of
an associated Fredholm integral equation.
Index Terms-- Extrapolation, Spherical Harmonics, Modelim-
ited.
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