A Fourier-invariant method for locating point-masses and computing their attributes

Charles K. Chui; H. N. Mhaskar

doi:10.1016/j.acha.2017.08.010

A Fourier-invariant method for locating point-masses and computing their attributes

Charles K. Chui
, H. N. Mhaskar^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Letter › peer-review

6 Citations (Scopus)

Abstract

Motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting point-masses, determining their spatial locations, and computing their attributes. Based on computation of Hermite moments that are Fourier-invariant, our approach facilitates the processing of both spatial and Fourier data in any dimension.

Original language	English
Pages (from-to)	436-452
Number of pages	17
Journal	Applied and Computational Harmonic Analysis
Volume	45
Issue number	2
DOIs	https://doi.org/10.1016/j.acha.2017.08.010
Publication status	Published - Sept 2018

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User-Defined Keywords

Hermite moments
Localized kernels
Point mass separation
Polynomial frames

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10.1016/j.acha.2017.08.010

Cite this

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title = "A Fourier-invariant method for locating point-masses and computing their attributes",

abstract = "Motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting point-masses, determining their spatial locations, and computing their attributes. Based on computation of Hermite moments that are Fourier-invariant, our approach facilitates the processing of both spatial and Fourier data in any dimension.",

keywords = "Hermite moments, Localized kernels, Point mass separation, Polynomial frames",

author = "Chui, \{Charles K.\} and Mhaskar, \{H. N.\}",

note = "Funding Information: This author is also associated with the Statistics Department of Stanford University, CA 94305, and his research is partially supported by U.S. ARO Grant W911NF-15-1-0385, Hong Kong Research Council Grant \# GRF-12300917 and Hong Kong Baptist University Grant \# HKBU-RC-ICRS/16-17/03. Publisher copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2018",

month = sep,

doi = "10.1016/j.acha.2017.08.010",

language = "English",

volume = "45",

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journal = "Applied and Computational Harmonic Analysis",

issn = "1063-5203",

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TY - JOUR

T1 - A Fourier-invariant method for locating point-masses and computing their attributes

AU - Chui, Charles K.

AU - Mhaskar, H. N.

N1 - Funding Information: This author is also associated with the Statistics Department of Stanford University, CA 94305, and his research is partially supported by U.S. ARO Grant W911NF-15-1-0385, Hong Kong Research Council Grant # GRF-12300917 and Hong Kong Baptist University Grant # HKBU-RC-ICRS/16-17/03. Publisher copyright: © 2017 Elsevier Inc.

PY - 2018/9

Y1 - 2018/9

N2 - Motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting point-masses, determining their spatial locations, and computing their attributes. Based on computation of Hermite moments that are Fourier-invariant, our approach facilitates the processing of both spatial and Fourier data in any dimension.

AB - Motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting point-masses, determining their spatial locations, and computing their attributes. Based on computation of Hermite moments that are Fourier-invariant, our approach facilitates the processing of both spatial and Fourier data in any dimension.

KW - Hermite moments

KW - Localized kernels

KW - Point mass separation

KW - Polynomial frames

UR - https://www.scopus.com/pages/publications/85031494421

U2 - 10.1016/j.acha.2017.08.010

DO - 10.1016/j.acha.2017.08.010

M3 - Letter

AN - SCOPUS:85031494421

SN - 1063-5203

VL - 45

SP - 436

EP - 452

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

IS - 2

ER -

A Fourier-invariant method for locating point-masses and computing their attributes

Abstract

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