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Solving ill-posed problems with mollification and an application in biometrics
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2018 (English)Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
##### Abstract [en]

This is a thesis about how molliﬁcation can be used as a regularization method to reduce noise in ill-posed problems in order to make them well-posed. Ill-posed problems are problems where noise get magniﬁed during the solution process. An example of this is how measurement errors increases with diﬀerentiation. To correct this we use molliﬁcation.

Molliﬁcation is a regularization method that uses integration or weighted average to even out a noisy function. The diﬀerent types of error that occurs when mollifying are the truncation error and the propagated data error. We are going to calculate these errors and see what aﬀects them. An other thing worth investigating is the ability to diﬀerentiate a molliﬁed function even if the function itself can not be diﬀerentiated.

An application to molliﬁcation is a blood vessel problem in biometrics where the goal is to calculate the elasticity of the blood vessel’s wall. To do this measurements from the blood and the blood vessel are required, as well as equations for the calculations. The model used for the calculations is ill-posed with regard to speciﬁc variables which is why we want to apply molliﬁcation. Here we are also going to take a look at how the noise level aﬀects the ﬁnal result as well as the molliﬁcation radius.

2018. , p. 45
##### Keywords [en]
Mollification, regularization, ill-posed problems, biometrics, blood vessel
Mathematics
##### Identifiers
ISRN: LiTH-MAT-EX--2018/02-SEOAI: oai:DiVA.org:liu-145539DiVA, id: diva2:1187676
Mathematics
##### Examiners
Available from: 2018-03-05 Created: 2018-03-05 Last updated: 2018-03-06Bibliographically approved

#### Open Access in DiVA

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##### By organisation
Mathematics and Applied MathematicsFaculty of Science & Engineering
Mathematics

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Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• oxford
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
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