Inversion of the heat equation by a block based algorithm using spline wavelet packets

Amir Averbuch, Pekka Neittaanmäki, Valery Zheludev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present a robust algorithm starting from 1D or 2D discrete noised data to approximately invert the heat equation, which is an ill-conditioned problem. Relative contributions of the coherent structure and the noise in different frequency bands of the available data are different. We propose to solve the inversion problem separately in different frequency bands by methods similar to the Tikhonov regularization. This separation is achieved by using spline wavelet packets. The solutions are derived as linear combinations of those wavelet packets.

Original languageEnglish
Title of host publicationNumerical Methods for Differential Equations, Optimization, and Technological Problems
EditorsSergey Repin, Timo Tiihonen, Tero Tuovinen
PublisherSpringer Netherland
Pages219-236
Number of pages18
ISBN (Print)9789400752870
DOIs
StatePublished - 2013
EventECCOMAS Thematic Conference Computational Analysis and Optimization, CAO 2011 - Jyvaskyla, Finland
Duration: 9 Jun 201111 Jun 2011

Publication series

NameComputational Methods in Applied Sciences
Volume27
ISSN (Print)1871-3033

Conference

ConferenceECCOMAS Thematic Conference Computational Analysis and Optimization, CAO 2011
Country/TerritoryFinland
CityJyvaskyla
Period9/06/1111/06/11

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