A fast Hermite transform

被引：25
|
作者：
Leibon, Gregory [1 ]
Rockmore, Daniel N. [1 ,2 ]
Park, Wooram [3 ]
Taintor, Robert [1 ]
Chirikjian, Gregory S. [3 ]
机构：
[1] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA
[2] Dartmouth Coll, Dept Comp Sci, Hanover, NH 03755 USA
[3] Johns Hopkins Univ, Dept Mech Engn, Baltimore, MD 21218 USA
来源：
THEORETICAL COMPUTER SCIENCE | 2008年 / 409卷 / 02期
关键词：
Generalized Fourier transform; Hermite transform; Orthogonal polynomial transform; Three-term recurrence; Tomographic reconstruction; Protein structure;
D O I：
10.1016/j.tcs.2008.09.010
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We present algorithms for fast and stable approximation of the Hermite transform of a compactly supported function on the real line, attainable via an application of a fast algebraic algorithm for computing sums associated with a three-term relation. Tradeoffs between approximation in bandlimit (in the Hermite sense), and size of the support region are addressed. Numerical experiments are presented that show the feasibility and utility of our approach. Generalizations to any family of orthogonal polynomials are outlined. Applications to various problems in tomographic reconstruction, including the determination of protein structure, are discussed. (C) 2008 Elsevier B.V. All rights reserved.
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页码：211 / 228
页数：18
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