A fast Hermite transform

被引：26
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
  • [31] Rotation-invariant texture features from the steered Hermite transform
    Estudillo-Romero, Alfonso
    Escalante-Ramirez, Boris
    PATTERN RECOGNITION LETTERS, 2011, 32 (16) : 2150 - 2162
  • [32] Coefficient Thresholding in the Gradient Reconstruction Algorithm for Signals Sparse in the Hermite Transform Basis
    Brajovic, Milos
    Vujovic, Stefan
    Orovic, Irena
    Stankovic, Srdjan
    APPLICATIONS OF INTELLIGENT SYSTEMS, 2018, 310 : 30 - 41
  • [33] Heart Rate Estimation using Hermite Transform Video Magnification and Deep Learning
    Moya-Albor, Ernesto
    Brieva, Jorge
    Ponce, Hiram
    Rivas-Scott, Orlando
    Gomez-Pena, Cristina
    2018 40TH ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY (EMBC), 2018, : 2595 - 2598
  • [34] A Robust and Secure Watermarking Approach Based on Hermite Transform and SVD-DCT
    Gomez-Coronel, Sandra L. L.
    Moya-Albor, Ernesto
    Brieva, Jorge
    Romero-Arellano, Andres
    APPLIED SCIENCES-BASEL, 2023, 13 (14):
  • [35] Detection of rregular QRS Complexes using Hermite Transform and Support Vector Machine
    Vulaj, Zoja
    Brajovic, Milos
    Draganic, Andela
    Orovic, Irena
    PROCEEDINGS OF 2017 INTERNATIONAL SYMPOSIUM ELMAR, 2017, : 59 - 62
  • [36] SAR-image classification with a directional-oriented Discrete Hermite Transform
    Escalante-Ramírez, B
    López-Quiroz, P
    Silván-Cárdenas, JL
    IMAGE AND SIGNAL PROCESSING FOR REMOTE SENSING VIII, 2003, 4885 : 234 - 245
  • [37] Compressive Sensing of Signals Sparse in 2D Hermite Transform Domain
    Brajovic, Milos
    Orovic, Irena
    Dakovic, Milos
    Stankovic, Srdan
    PROCEEDINGS OF ELMAR 2016 - 58TH INTERNATIONAL SYMPOSIUM ELMAR 2016, 2016, : 169 - 172
  • [38] Watermarked cardiac CT image segmentation using deformable models and the Hermite transform
    Gomez-Coronel, Sandra L.
    Moya-Albor, Ernesto
    Escalante-Ramirez, Boris
    Brieva, Jorge
    10TH INTERNATIONAL SYMPOSIUM ON MEDICAL INFORMATION PROCESSING AND ANALYSIS, 2015, 9287
  • [39] S-transform and Hermite transform of Hilbert space-valued stochastic distributions with applications to stochastic differential equations
    Melnikova, I. V.
    Alshanskiy, M. A.
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2011, 22 (4-5) : 293 - 301
  • [40] The Hermite transform as an efficient model for local image analysis:: An application to medical image fusion
    Escalante-Ramirez, Boris
    COMPUTERS & ELECTRICAL ENGINEERING, 2008, 34 (02) : 99 - 110
12345