A Reconstruction Method for Band-Limited Signals on the Hyperbolic Plane

Details A Reconstruction Method for Band-Limited Signals on the Hyperbolic Plane A Reconstruction Method for Band-Limited Signals on the Hyperbolic Plane

2011-05-14

arxiv.org/abs/1105.2858v1

Sampling Theory in Signal and Image Processing Vol. 4, No. 2, May. 2005, pp. 107-119

Mathematics

Functional Analysis

Scientific paper

A notion of band limited functions is considered in the case of the hyperbolic plane in its Poincare upper half-plane $\mathbb{H}$ realization. The concept of band-limitedness is based on the existence of the Helgason-Fourier transform on $\mathbb{H}$. An iterative algorithm is presented, which allows to reconstruct band-limited functions from some countable sets of their values. It is shown that for sufficiently dense metric lattices a geometric rate of convergence can be guaranteed as long as the sampling density is high enough compared to the band-width of the sampled function.

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