A class of solutions for the inverse diffusion problem

J. Lewalle

doi:10.1016/S0893-9659(00)00203-2

A class of solutions for the inverse diffusion problem

J. Lewalle

Department of Mechanical & Aerospace Engineering

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

3 Scopus citations

Abstract

The close relation between Hermitian wavelets transforms and the diffusion equation is used to derive a one-parameter family of distributed sources as solutions to the inverse diffusion problem in R^N × R_. The class of solutions is interpreted in terms of energetically dominant events in the wavelet representation, where the scale of the event is proportional to its age. The construction procedure is a straightforward extension of the inverse wavelet transform formula. Simple examples illustrate the method.

Original language	English (US)
Pages (from-to)	617-624
Number of pages	8
Journal	Applied Mathematics Letters
Volume	14
Issue number	5
DOIs	https://doi.org/10.1016/S0893-9659(00)00203-2
State	Published - Jul 2001

Keywords

Inverse diffusion
Source distribution
Wavelets

ASJC Scopus subject areas

Applied Mathematics

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10.1016/S0893-9659(00)00203-2

Cite this

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title = "A class of solutions for the inverse diffusion problem",

abstract = "The close relation between Hermitian wavelets transforms and the diffusion equation is used to derive a one-parameter family of distributed sources as solutions to the inverse diffusion problem in RN × R_. The class of solutions is interpreted in terms of energetically dominant events in the wavelet representation, where the scale of the event is proportional to its age. The construction procedure is a straightforward extension of the inverse wavelet transform formula. Simple examples illustrate the method.",

keywords = "Inverse diffusion, Source distribution, Wavelets",

author = "J. Lewalle",

note = "Funding Information: Partial support for this work was provided by the U S NatIonal Science Foundation under Grant CTS-9819796 {\textquoteleft}For the clarity of notations and to reserve famlhar subscnpts for vector fields, presubscrlpts will be used to denote Gaussian filtering as m ou(C, I) or the related Hernutlan wavelet transforms of order n > 0, as m ,,u(C, z) below",

year = "2001",

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AU - Lewalle, J.

N1 - Funding Information: Partial support for this work was provided by the U S NatIonal Science Foundation under Grant CTS-9819796 ‘For the clarity of notations and to reserve famlhar subscnpts for vector fields, presubscrlpts will be used to denote Gaussian filtering as m ou(C, I) or the related Hernutlan wavelet transforms of order n > 0, as m ,,u(C, z) below

PY - 2001/7

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N2 - The close relation between Hermitian wavelets transforms and the diffusion equation is used to derive a one-parameter family of distributed sources as solutions to the inverse diffusion problem in RN × R_. The class of solutions is interpreted in terms of energetically dominant events in the wavelet representation, where the scale of the event is proportional to its age. The construction procedure is a straightforward extension of the inverse wavelet transform formula. Simple examples illustrate the method.

AB - The close relation between Hermitian wavelets transforms and the diffusion equation is used to derive a one-parameter family of distributed sources as solutions to the inverse diffusion problem in RN × R_. The class of solutions is interpreted in terms of energetically dominant events in the wavelet representation, where the scale of the event is proportional to its age. The construction procedure is a straightforward extension of the inverse wavelet transform formula. Simple examples illustrate the method.

KW - Inverse diffusion

KW - Source distribution

KW - Wavelets

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DO - 10.1016/S0893-9659(00)00203-2

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AN - SCOPUS:0035389074

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VL - 14

SP - 617

EP - 624

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 5

ER -

A class of solutions for the inverse diffusion problem

Abstract

Keywords

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