College of Computer Science and Mathematics

Discussion of a master’s thesis in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“An Improved Conjugate Gradient Methods For Solving Unconstrained Optimization Problems And Images Restoration “

It was discussed in the discussion hall of Computer Science and Mathematics at the University of Mosul on sunday 27 2025/7/.

master’s thesis by Ruaa Zaki Mahmood Al-Dabagh 

under the supervision of Asst. Prof. Dr. Hisham Mohammed Khader

This thesis presents an in-depth study of conjugate gradient algorithms and their optimization for applications in unconstrained optimization and image restoration. The first chapter establishes the fundamentals of optimization, including the classification of optimization problems (constrained and unconstrained), concepts of local and global minima, gradient vectors, Hessian matrices, and discussions of fundamental algorithms such as steepest descent, Newton’s method, and quasi-Newton methods.  In the second and third chapters, two novel algorithms (RH2 and RH1) are introduced, relying on innovative conjugate coefficients to enhance numerical efficiency. These algorithms are compared with the traditional TTFR method, demonstrating the superiority of the proposed algorithms in reducing the number of iterations and function evaluations. Additionally, the descent and convergence properties of the proposed algorithms are rigorously proven under specific assumptions. The fourth chapter focuses on applying these algorithms to restore images corrupted by impulse noise (e.g., salt-and-pepper noise). Using metrics such as the peak signal-to-noise ratio (PSNR), RH2 and RH1 achieve higher values compared to TTFR, particularly under high noise levels of up to 90%. This work underscores the importance of integrating theoretical insights with computational techniques to develop practical solutions for complex optimization challenges.

The scientific committee included the following members:

• Dr. Basim Abbas Hassan Abdulrahman -Chairman
• Dr. Hamsa Tharwat Saeed – Member
• Dr. Eman Tarek Hamed – Member
• . Asst. Prof. Dr. Hisham Mohammed Khader – Member and supervisor.