College of Computer Science and Mathematics

Discussion of a Doctoral Dissertation in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“ Some New Conjugate Gradient Methods To Reduce Images Noise “

In continuation of the scientific research movement and with the follow-up and presence of the Dean of the College of Computer Science and Mathematics

   Prof. Dr. Duha Bashir Abdullah The esteemed

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Monday  12-8-2024

Doctorial Dissertation by student Ali Ahmed Abdul Raheem Abdulla

, under the supervision of  Prof. Dr. Prof. Dr. Basim Abbas Hassan (Supervisor)

Optimization is a very developed area with its wide applications in different sciences, especially it has applications in various fields such as, analysis and processing image. it is important to understand the efficiency of optimization algorithms for practical applications. This dissertation investigates significant issues and create efficient optimization models and some new optimization algorithms and applies them to practical problems, mainly for noise removal of images.

The conjugate gradient method is one of the crucial methods frequently used to tackle unconstrained optimization problems; thus, we investigate the method’s efficacy in resolving actual issues in the field of image processing. In this thesis, a new conjugate gradient (CG) method is proposed; the method’s derivation is based on quadratic models and conjugacy conditions. The suggested methods have the appealing quality that the search direction created at each iteration is descending, whether exact or imprecise line searches are used. Global convergence of the proposed methods is also established when strong Wolfe conditions are used. The numerical outcomes demonstrate that, when using four test photos, the new formulas are more effective than the Fletcher-Reeves technique. To prove the viability of the suggested methods, comparison experiments on impulse noise removal are given.

The main objective of the thesis was to show the computational efficiency of new conjugate gradient algorithms for noise reduction in images. The conclusion of the thesis discusses the new findings and offers some recommendations for how to use them forward.

The scientific committee included the following members:

• Dr. Ban Ahmed Hassan – Chairman.
• Dr. Shahbaa Ibrahim Khaleel – Member.
• Dr. Hamsa Tharwat Saeed – Member.
• Prof. Dr. Hawraz Nadem Jabar – Member
• Prof. Dr. Edrees Mohamed Nori – Member.
• Dr. Basim Abbas Hassan -Member & Supervisor.