TWO-LEVEL METHOD FOR IMAGE DEBLURRING PROBLEM

TWO-LEVEL METHOD FOR IMAGE DEBLURRING PROBLEM. PhD thesis, King Fahd University of Petroleum and Minerals.

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Arabic Abstract

ً ايضاير فصوت (ةيلص ٔ الا ةروصلا) u و (ةلجسم ةروص) z نيب ةقالعلا .روصلا حوض و مدع و هيبابض ةلازٕ ا ةلٔ اسمل ةيددعلا لولحلا ةلاسرلا هذه لوانتت ؛ يلاتلا وحنلا ىلع z = Ku + ϵ (2) ةلتعم حبصت ةلٔ اسملا نٕ اف يلاتلابو ، جمدم ليغشت لماع K ربتعي ةلٔ اسملا ةذه يف .هيبابضلا لغشمو لماع وه K و ءاضوض ةلاد ϵ نوكي ثيح (TV) يلكلا فالتخالا ةيوست لثم ةيماظتنا فئاظو مادختسا وه تاجالعلا حٔ ا .ةرقتسم تسيل ةروصلا ةيبابض ةلاز ٕ ا ةلٔ اسم نٕ اف يلاتلابو .ً ايضاير نكلو .ىرخ ٔالا ةفيطللا صئاصخلا نم ديدعلا اهلو ةروصلا ةداعتسا لئاسم يف ا ً دج ةلاعف جذامنلا هذه .كلذ ىلٕ ا ام (MC) طسوتملا ءانحنا ةيوستوMC ةلاح يف .ةلاعف ةيمقر ةيمزراوخ ريوطت دقعي امم هجردلا ةيلاع تاقتشم نمضتت ةيوستلا جذامنب ةطبترملا جنارغال رليؤ ا تالداعم كيكفت ن ٕ اف ،يه يطخلا ريغ ماظنلا اذهل ةيبوقعيلا ةفوفصملا .ةدقعم ةيطخ ريغ تالداعم ماظن جتنت ةعبارلا هجردلا نم تاقتشم جنارغال رليؤ ا تالداعم نمضتت ،هذه يف .ةمساح ةيضق ةلاعفلا ةيددعلا ةقيرطلا ريوطت دعي ، هجردلا ةيلاع تاقتشملاو ةيلاعلا ةيطخلا مدع ببسب .ةلتكتمو ريبك قاطن تاذ ةفوفصم طسوتملا ءانحنا ةيوستو (TV) يلكلا فالتخالا ةيوست جذامنل ً ةصاخ روصلا ةيبابض ةلازٕ ا ةلكشمل نييوتسم نم ةيوقو ةلاعف ةقيرط مدقن ، ةحورطٔ الا ريغص ددع ىلع يوتحت ةروص ىلع ، هجردلا يلاع قتشم ، يطخ ريغ ريغص ماظن ىل ٕ ا هلٔ اسملا ريغصت قيرط نع نييوتسملا تاذ ةقيرطلا ٔ ادبت (MC) .(يناثلا ىوتسملا ) لسكبلا تادحو نم ريبك ددع عم ، هضفخنم هجرد وذ قتشم ، ةفلكت لقٔ ا يطخ ماظنو (لو ٔ الا ىوتسملا) لسكبلا تادحو نم فالتخالا ةيوست ىلٕ ا ةدنتسملا جذامنلل ءاطخ ٔالا ليلحت ةسارد مت امك .ةغيصلا ضرعو يناثلا ىوتسملل ىلثملا ةيوستلا لماعم قاقتشا ةسارد تمت امكانضرعو نيبوتسملا تاذ ةقيرط مادختساب ةيمقر روص ةدعل ةيبابضلا انلزٔ ا كلذكو، هقيرطلا ةءافك تابث ٕ ال (MC) طسوتملا ءانحنا ةيوستو (TV) يلكلا .مهل ةيددعلا جئاتنلا

English Abstract

DISSERTATION ABSTRACT NAME: Shahbaz Ahmad TITLE OF STUDY: Two-Level Method For Image Deblurring Problem MAJOR FIELD: Mathematics DATE OF DEGREE: April 2020 This 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 image deblurring 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.

Item Type: Thesis (PhD)
Subjects: Math
Department: College Of Sciences > Mathematical Science Dept
Committee Advisor: Fairag, Faisal
Committee Members: Mustapha, Kassem and Bokhari, Ashfaq Hussain and Yousuf, Muhammad
Depositing User: SHAHBAZ AHMAD (g201410020)
Date Deposited: 29 Apr 2021 10:21
Last Modified: 29 Apr 2021 10:21
URI: https://eprints.kfupm.edu.sa/id/eprint/141850