Αντίστροφα προβλήματα-Ανακατασκευή εικόνας με ολοκληρωτικές εξισώσεις Fredholm πρώτου είδους

Πάντου, Κυριακή; Pantou, Kyriaki

dc.contributor.author	Πάντου, Κυριακή	el
dc.contributor.author	Pantou, Kyriaki	en
dc.date.accessioned	2017-11-24T11:59:13Z
dc.date.available	2017-11-24T11:59:13Z
dc.date.issued	2017-11-24
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/45956
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.14862
dc.rights	Default License
dc.subject	Αντίστροφα προβλήματα	el
dc.subject	Inverse problems	en
dc.subject	Fredholm 1st integral equation	en
dc.subject	Incorrectly fixed problems	en
dc.subject	Riemann-Lebesque entry	en
dc.subject	Discrete methods	en
dc.subject	Normalization methods	en
dc.subject	Picard condition	en
dc.subject	Singular value evaluation (SVE Method)	en
dc.subject	Singular value decomposition (SVD Method)	en
dc.subject	L-Curve	en
dc.subject	Image reconstruction	en
dc.title	Αντίστροφα προβλήματα-Ανακατασκευή εικόνας με ολοκληρωτικές εξισώσεις Fredholm πρώτου είδους	el
heal.type	bachelorThesis
heal.classification	Μαθηματικά	el
heal.language	el
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2017-05-25
heal.abstract	Αντίστροφα προβλήματα	el
heal.abstract	Inverse problems are the foundation for solving many other problems, many of which are included in our everyday life. In this study we mainly deal with the inverse problem which, with the help of the Fredholm 1st integral equation, will lead us to the analysis and reconstruction of an image. Beyond the theoretical part, we will see some applications of the inverse problem in image analysis with the appropriate algorithms. In the 1st part of the diploma thesis, we define the inverse problem and the ill posed problems. In the 2nd part of the paper, we focus on the complete Fredholm equation which is the first kind to solve the inverse problems, with the help of the Riemann-Lebesque entry we mention an example from the geophysics applied by the Fredholm equation. In the 3rd part of the paper, we analyse two ways of distinguishing the integral Fredholm equation, namely the quadrature method and the method of expansion. Finally, we analyse the role of the two most important methods, Singular Value Evaluation (SVE) and Singular Value Decomposition (SVD) on the inverse problems, as well as the contribution of the Picard Treaty. In the 4th part, we define and analyse the three ways of normalizing discrete systems and put more emphasis on how to solve the L-Curve curve. In the 5th part, we deal with the computational methods of normalization of discrete systems. In the 6th part of the study, we refer to the main part of the work, namely the clarification of an image, in which the CGLS algorithm will lead to the implementation of the image analysis, as we will see the example of tomography in two dimensions.Finally, in the 7th part, by executing the appropriate commands in MatLab, we will apply a specific algorithm image to reconstruct it.	en
heal.advisorName	Γκιντίδης, Δρόσος	el
heal.committeeMemberName	Χαραλαμπόπουλος, Αντώνιος	el
heal.committeeMemberName	Κυριάκη, Κυριακή	el
heal.academicPublisher	Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών. Τομέας Μαθηματικών	el
heal.academicPublisherID	ntua
heal.numberOfPages	73 σ.	el
heal.fullTextAvailability	true