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

“ Improvement of Conjugate Gradient Methods to Reduce Noise in Images “

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Thursday, 13 -3-2025.

Ph.D. Dissertation by Student Mohammed Wa’adullah Taha

under the supervision of Prof. Dr. Basim Abbas Hassan

 Recent developments in gradient-based methods have made it possible to use them more effectively in image restoration problems, leading to more accurate results. Iterative gradient methods represent an important class of methods for solving the image restoration problems described in this study. The most significant advantage of conjugate gradient methods is their low memory requirements and rapid convergence. The conjugate parameter plays an important role in improving conjugate gradient methods.

Several conjugate gradient formulas have been derived in the conjugate gradient method based on the second-order Taylor series and then used to construct a new curvature condition, taking advantage of the search direction properties of Newton’s method, the conjugation condition, and the Berry conjugation condition. Based on these formulas, we present new research directions for conjugate gradient methods for use in image restoration and impulse noise removal. These formulas rely on the values of the function and the gradient vectors at each iteration, which contributes to improving the efficiency of the methods and the accuracy of the convergence process to a solution. Under certain assumptions and using the Wolff research line, the overall regression and convergence properties of the given methods are discussed.

Numerical results demonstrate that the new methods have a high level of efficiency and accuracy in image reconstruction and convergence speed when compared to the known formula using some standard test images in this field.

The study concludes with a discussion of the new findings and some suggestions for future applications.

The scientific committee included the following members:

• Dr. Ban Ahmed Hassan – Chairman
• Dr. Shahbaa Ibrahim Khaleel – Member.
• Dr. Ghada Moayid Rasheed – Member.
• Dr. Hawraz Nazim Jabbar – Member.
• Prof. Dr. Edrees Mohammed Nori- Member.
• Dr. Basim Abbas Hassan – Member and supervisor.