Extragradient methods for elliptic inverse problems and image denoising

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dc.contributor.advisor Khan, Akhtar
dc.contributor.author Oleksyn, James
dc.date.accessioned 2011-09-15T17:08:31Z
dc.date.available 2011-09-15T17:08:31Z
dc.date.issued 2011-06-10
dc.identifier.uri http://hdl.handle.net/1850/14144
dc.description.abstract Numerous mathematical models in applied mathematics can be expressed as a partial differential equation involving certain coefficients. These coefficients are known and they describe some physical properties of the model. The direct problem in this context is to solve the partial differential equation. By contrast, an inverse problem asks for the identification of the variable coefficients when a certain measurement of a solution of the partial differential equation is available. One of the most commonly used approaches for solving this inverse problem is by posing a constrained minimization problem which can be written as a variational inequality. The main contribution of this thesis is to employ various variants of extragradient methods to solve the inverse problem of parameter identification by posing it as a variational inequality. We present a thorough comparison of projected gradient method, scaled projected gradient method and several extragradient methods including the Marcotte variants, He-Goldstein type method, the projection- contraction methods proposed by Solodov and Tseng, and the hyperplane method developed by Iusem. We also test the performance of the extragradient methods for the image debluring problem. en_US
dc.language.iso en_US en_US
dc.subject Extragradient en_US
dc.subject Inverse problem en_US
dc.subject Parameter identification en_US
dc.subject Projected gradient method en_US
dc.subject Regularization en_US
dc.subject.lcc TA1637 .O54 2011
dc.subject.lcsh Image processing--Mathematics en_US
dc.subject.lcsh Inverse problems (Differential equations) en_US
dc.title Extragradient methods for elliptic inverse problems and image denoising en_US
dc.type Thesis en_US
dc.description.college College of Science en_US
dc.description.department School of Mathematical Sciences en_US

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