A Matching Pursuit for the Sphere Based on the Poisson Semigroup

被引：0
|
作者：
Bernhard G. Bodmann
机构：
[1] University of Houston,Department of Mathematics
来源：
Sampling Theory in Signal and Image Processing | 2003年 / 2卷 / 2期
关键词：
Hilbert spaces with reproducing kernel; harmonic Hardy space; greedy sampling algorithm;
D O I：
10.1007/BF03549393
中图分类号：
学科分类号：
摘要：
An iterative greedy sampling and reconstruction algorithm for square-integrable functions on the two-sphere is presented. The algorithm performs a decomposition based on reproducing kernel spaces related to the Poisson semigroup. This decomposition starts from the harmonic extension of the initial function to the ball. In each iteration step, the respective input function is sampled in the ball and a multiple of a suitably chosen kernel function is subtracted. We discuss the rate of convergence for the reconstruction of functions that have harmonic extensions with finite gradient norm in the ball.
引用
收藏
页码：191 / 205
页数：14
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