Two-level Method For Image Deblurring Problem

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علوم بحتة وطبيعية

الملخص

DISSERTATION ABSTRACTNAME: Shahbaz AhmadTITLE OF STUDY: Two-Level Method For Image Deblurring ProblemMAJOR FIELD: MathematicsDATE OF DEGREE: April 2020This thesis deals with numerical solutions to image deblurring problem. Mathematically, the relationship between z (recorded image) and u (original image) is as follow;z = Ku + ϵ (1)where ϵ is a noise function and K is blurring operator. Here K is a compact operator, so the problem becomes ill-posed. Thus image deblurring problem is not stable. One remedy is to use a regularizational functionals such as total variation (TV) regularization and mean curvature (MC) regularization etc. These models are very effective in image restoration problems and they have many other nice properties. But, the discretization of the associated Euler-Lagrange equations of regularization models involve high order derivatives which complicate developing an efficient numerical algorithm. In case of MC, Euler-Lagrange equations involve fourth order derivatives which produce complicate nonlinear system of equations. The Jacobian matrix of this nonlinear system is block banded matrix with large bandwidth. Due to high nonlinearity and high order derivative, the development of the efficient numerical method is a crucial issue.In this thesis, we introduce an efficient and robust Two-Level method for imagedeblurring problem especially for TV and MC base models. The Two-Level method started by reducing the problem to one small nonlinear system, having high order derivative, on image with small number of pixels (Level-I) and one less expensive system, having low order derivative, with large number of pixels (Level-II). The derivation of the optimal regularization parameter of Level-II is also studied and formula is presented. The error analysis for TV and MC based models are also developed. To demonstrate the efficiency of the Two-Level method, numerical results are also presented.

روابط وملفات

التعريف والنوع

رقم الوثيقة

09edb4b3-7c3d-4a00-a598-d577bfdf6ff3

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل دكتوراة

نوع الملف

pdf text

أسماء الملفات

848337_1.pdf

بيانات النشر

ترجمة العنوان

الطريقة ثنائية المستوي لمسالة إزالة ضبابية الصور الرقمية

ألقاب المؤلفين

[{"name_ar":"Faisal Fairag ","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"Ke Chen ","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"شهباز احمد","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

English

المصدر والدورية

اسم المصدر

Two-level Method For Image Deblurring Problem

المحتوى والصفحات

عدد الصفحات

0

كلمات الباحثين

Math

إشراف وإعداد

الإشراف

Faisal Fairag , Ke Chen

الإعداد

شهباز احمد

الاقتباسات الببليوغرافية