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.
引用
收藏
页码：211 / 228
页数：18
相关论文
共 50 条
  • [21] Compressive Sensing Approach in the Hermite Transform Domain
    Stankovic, Srdjan
    Stankovic, Ljubisa
    Orovic, Irena
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2015, 2015
  • [22] On a Hermite transform in spaces of generalized functions on Rn
    Glaeske, HJ
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2002, 13 (03) : 309 - 319
  • [23] The multiscale hermite transform for local orientation analysis
    Silván-Cárdenas, JL
    Escalante-Ramírez, B
    IEEE TRANSACTIONS ON IMAGE PROCESSING, 2006, 15 (05) : 1236 - 1253
  • [24] Optic flow estimation using the hermite transform
    Escalante-Ramírez, B
    Silván-Cárdenas, JL
    Yuen-Zhou, H
    APPLICATIONS OF DIGITAL IMAGE PROCESSING XXVII, PTS 1AND 2, 2004, 5558 : 632 - 643
  • [25] Identification of phytoplankton species using Hermite transform
    Castro-Valdez, A.
    Alvarez-Borrego, J.
    UKRAINIAN JOURNAL OF PHYSICAL OPTICS, 2018, 19 (02) : 106 - 120
  • [26] FHSS signal sparsification in the Hermite transform domain
    Brajovic, Milos
    Draganic, Andjela
    Orovic, Irena
    Stankovic, Srdjan
    2016 24TH TELECOMMUNICATIONS FORUM (TELFOR), 2016, : 471 - 474
  • [27] A fast algorithm for multivariate Hermite interpolation
    LEI Na
    TENG Yuan
    REN Yu-xue
    AppliedMathematics:AJournalofChineseUniversities(SeriesB), 2014, 29 (04) : 438 - 454
  • [28] Correction: Restriction theorem for the Fourier–Hermite transform and solution of the Hermite–Schrödinger equation
    Shyam Swarup Mondal
    Jitendriya Swain
    Advances in Operator Theory, 2023, 8
  • [29] A fast algorithm for multivariate Hermite interpolation
    Na Lei
    Yuan Teng
    Yu-xue Ren
    Applied Mathematics-A Journal of Chinese Universities, 2014, 29 : 438 - 454
  • [30] A fast algorithm for multivariate Hermite interpolation
    LEI Na
    TENG Yuan
    REN Yu-xue
    Applied Mathematics:A Journal of Chinese Universities, 2014, (04) : 438 - 454
12345