James Oleksyn

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.

Library of Congress Subject Headings

Image processing--Mathematics; Inverse problems (Differential equations)

Publication Date

6-10-2011

Document Type

Thesis

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

Khan, Akhtar

Comments

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: TA1637 .O54 2011

Campus

RIT – Main Campus

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