5425
dtolah@pmu.edu.sa
S008
Dr. Danyh Tolah is an Assistant Professor of Mathematics at Prince Mohammad Bin Fahd University (PMU). She earned her Ph.D. in Applied Mathematics from Arizona State University in 2025. Her research focuses on inverse problems, computational imaging, numerical linear algebra, and numerical optimization, with particular interests in image restoration, image deblurring, edge-preserving regularization, wavelet-based multilevel methods, and tomographic imaging.
Her research involves the development and analysis of efficient numerical methods for large-scale discrete ill-posed inverse problems. Her doctoral work focused on edge-preserving multilevel methods for signal and image restoration, including wavelet-based approaches for image deblurring. Her current work continues to develop numerical methods for inverse problems while extending these approaches to broader computational imaging applications.
Dr. Tolah has experience teaching undergraduate mathematics courses including applied linear algebra, differential equations, precalculus, and calculus for engineers. In teaching, she emphasizes conceptual understanding, mathematical reasoning, and the connection between mathematical theory and computational applications. Her future research aims to advance efficient and reliable numerical methods for inverse problems, image reconstruction, and computational imaging.
Ph.D. in Applied Mathematics, Arizona State University, Tempe, Arizona, USA, 2025
M.A. in Applied Mathematics, Arizona State University, Tempe, Arizona, USA, 2024
M.Sc. in Mathematics, Taibah University, Madinah, Saudi Arabia, 2013
B.Sc. in Mathematics, Taibah University, Madinah, Saudi Arabia, 2008
Manuscripts Under Review
Tolah, D., & Español, M. I. (2026). Wavelet-based multilevel Split Bregman methods for edge-preserving image deblurring. Manuscript under review.
Tolah, D., Español, M. I., & Kilmer, M. E. (2026). Wavelet-based multilevel framework for ℓ₁-regularized image deblurring. Manuscript under review. Preprint available on arXiv: 2608.17123.
Other
Tolah, D. (2025). Edge-preserving multilevel methods for discrete ill-posed inverse problems (Publication No. 32284564) [Doctoral dissertation, Arizona State University]. ProQuest Dissertations & Theses Global.
Prince Mohammad Bin Fahd University (PMU), Assistant Professor of Mathematics
Society for Industrial and Applied Mathematics (SIAM), Member
American Mathematical Society (AMS), Member
Association for Women in Mathematics (AWM), Member
Current Research
My research focuses on the development of numerical methods for inverse problems and computational imaging. Current work includes image reconstruction and restoration, edge-preserving regularization, wavelet-based multilevel methods, numerical optimization, and large-scale computational problems. I am also extending my research toward tomographic imaging and broader inverse-problem applications.
Research Publications and Manuscripts
My recent research includes two manuscripts currently under review on wavelet-based multilevel methods for edge-preserving image deblurring. One of these works is also available as an arXiv preprint. My doctoral dissertation, Edge-Preserving Multilevel Methods for Discrete Ill-Posed Inverse Problems, was completed at Arizona State University in 2025 and is available through ProQuest Dissertations & Theses Global.
Research Presentations
My research has been presented at national and regional conferences, including the SIAM Conference on Computational Science and Engineering (2025), the Arizona Women’s Symposium in Mathematics (2024), and the SIAM Conference on Imaging Science (2024). These presentations focused on edge-preserving multilevel methods for image and signal restoration.
Teaching Associate / Instructor, Arizona State University, Tempe, Arizona, USA, January 2022 – December 2025
Taught and supported undergraduate and graduate mathematics courses, including Applied Linear Algebra, Modern Differential Equations, Precalculus, Calculus for Engineers I, Numerical Analysis I, Partial Differential Equations, Mathematical Structures, and Introductory Applied Statistics. Responsibilities included delivering lectures, leading recitation and discussion sessions, developing course materials and assessments, grading, and providing academic support to students.
Research Associate (Part-Time), Arizona State University, Tempe, Arizona, USA, February 2026 – Present
Conduct collaborative research in numerical methods for inverse problems and computational imaging, including image restoration and large-scale reconstruction problems. Develop and test computational algorithms and contribute to the preparation of research manuscripts.
Assistant Professor of Mathematics, Prince Mohammad Bin Fahd University (PMU), Dhahran, Saudi Arabia, August 2026 – Present
Teach undergraduate mathematics courses and conduct research in applied and computational mathematics, with interests in inverse problems, computational imaging, numerical linear algebra, image reconstruction and restoration, and related numerical methods.
Prince Mohammad Bin Fahd University (2026–Present)
Introductory Algebra — Instructor
Arizona State University (2022–2025)
MAT 343 – Applied Linear Algebra — Instructor
MAT 275 – Modern Differential Equations — Instructor / Teaching Assistant
MAT 170 – Precalculus — Instructor
MAT 265 – Calculus for Engineers I — Instructor
MAT 423 – Numerical Analysis I — Teaching Assistant
MAT 476 – Partial Differential Equations — Teaching Assistant
STP 420 – Introductory Applied Statistics — Grader
MAT 300 – Mathematical Structures — Grader
My research interests lie broadly in applied and computational mathematics, with a primary focus on inverse problems, computational imaging, numerical linear algebra, and numerical optimization. I am particularly interested in developing efficient and stable numerical methods for recovering information from incomplete, noisy, or degraded data. My research includes image reconstruction and restoration, image deblurring, edge-preserving regularization, wavelet-based sparse representations, and multilevel numerical methods. I am also interested in tomographic imaging and in extending inverse-problem methodologies to a broader range of computational imaging applications. My work explores iterative methods and efficient numerical solvers for large-scale discrete ill-posed problems, with particular attention to reconstruction accuracy, edge preservation, stability, and computational efficiency. My broader research interests include combining mathematical modeling, regularization techniques, and computational algorithms to address challenging imaging and reconstruction problems. I am also interested in future developments that connect classical model-based inverse-problem methods with data-driven and machine-learning approaches.
Society for Industrial and Applied Mathematics (SIAM) — Member
American Mathematical Society (AMS) — Member
Association for Women in Mathematics (AWM) — Member
