Discussion of Ph.D. Dissertation  in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“ Designed Some New Conjugate Gradient Algorithms to Restore Corrupted Images”

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Thursday, 10 -5-2026.

Ph.D. Dissertation by Yousif Ali Mohammed Ali

under the supervision of Prof. Dr. Basim Abbas Hassan Abdulrahman

The curvature condition plays a crucial role in improving both the global convergence and numerical efficiency of conjugate gradient algorithms, ensuring the regression characteristic of the search direction and achieving global convergence. These methods are preferred because it requires modest memory and has favourable convergence properties.

In this study, we derived various conjugate gradient methods using the second term of the Taylor series, an advanced formula within the family of nonlinear conjugate gradients, specifically designed for image denoising. Given the need for robust and computationally efficient algorithms capable of handling large-scale distorted images, the proposed methods improve convergence characteristics while reducing the computational load. Comprehensive numerical experiments were conducted using a set of standard images to evaluate the performance of the new methods compared to the well-known method. The results indicate that these methods consistently outperform the well-known method in key performance indicators, such as reducing the number of function evaluations, decreasing the number of iterations, and accelerating convergence speed. The new methods prove to be a highly effective alternative for processing distorted images.

The scientific committee included the following members:

• Dr. Abdulghafor Jassim Salim – Chairman
• Dr. Ghada Moayid Rasheed Al Naemi – Member.
• Dr. Hamsa Thrwat Saeed – Member.
• Dr. Hawraz Nazim Jabbar – Member.
• Prof. Dr. Hisham Mohammed Khudhur – Member.
• Dr. Basim Abbas Hassan Abdulrahman – Member and supervisor.