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DC Field | Value | Language |
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dc.date.accessioned | 2019-10-25T12:44:28Z | - |
dc.date.available | 2019-10-25T12:44:28Z | - |
dc.date.issued | 2019 | - |
dc.identifier.citation | Curmi, J. (2019). Approximate inverse for linear and non-linear inverse problems (Master’s dissertation). | en_GB |
dc.identifier.uri | https://www.um.edu.mt/library/oar/handle/123456789/47889 | - |
dc.description | M.SC.MATHS | en_GB |
dc.description.abstract | Many applications in science, engineering, medical imaging and industry arise, where specific results need to be inferred from a given set of observations. Such a task is called an inverse problem, which can be expressed by an operator equation of the form Af = g, where f is the unknown quantity under investigation, g is the measurement data, while A is a bounded operator, illustrating the relation between f and g. An added difficulty when trying to solve such problems is the fact that in most cases, the operator A is ill-posed in the Hadamard sense, meaning that the solution of such problems either does not exist, or is not unique, or else does not depend continuously on the data. As a result, various regularization techniques such as the method of approximate inverse were developed to overcome such issues. The aim of this dissertation is to analyze how the approximate inverse method can be used to reconstruct the unknown quantity f in the case of both linear and non-linear inverse problems. The focus of this dissertation will then shift to an in-depth analysis of a practical realization of the inverse conductivity problem, namely Electrical Impedance Tomography (EIT), in which the unknown complex admittivity has to be reconstructed. It will also be shown how the approximate inverse method can be applied to this same problem in order to reconstruct the unknown admittivity. | en_GB |
dc.language.iso | en | en_GB |
dc.rights | info:eu-repo/semantics/restrictedAccess | en_GB |
dc.subject | Inverse problems (Differential equations) | en_GB |
dc.subject | Electrical Impedance Tomography | en_GB |
dc.title | Approximate inverse for linear and non-linear inverse problems | en_GB |
dc.type | masterThesis | en_GB |
dc.rights.holder | The copyright of this work belongs to the author(s)/publisher. The rights of this work are as defined by the appropriate Copyright Legislation or as modified by any successive legislation. Users may access this work and can make use of the information contained in accordance with the Copyright Legislation provided that the author must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the prior permission of the copyright holder. | en_GB |
dc.publisher.institution | University of Malta | en_GB |
dc.publisher.department | Faculty of Science. Department of Mathematics | en_GB |
dc.description.reviewed | N/A | en_GB |
dc.contributor.creator | Curmi, Jeremy | - |
Appears in Collections: | Dissertations - FacSci - 2019 Dissertations - FacSciMat - 2019 |
Files in This Item:
File | Description | Size | Format | |
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19MSCMATH001.pdf Restricted Access | 2.29 MB | Adobe PDF | View/Open Request a copy |
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