Loading...
| Friend's email | |
| Your name | |
| Your email | |
| enter code | |
This page was sent successfuly
- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 57486 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Tefagh, Mojtaba; Hossein Khalaj, Babak
- Abstract:
- One of the common methods for cancer treatment is radiotherapy, which is used in combination with other treatment methods, such as surgery and chemotherapy, as one of the fundamental strategies in treating many cancer patients. This approach not only helps achieve more effective results in cancer treatment, but also enables patients to experience fewer side effects compared to other treatment methods and improves their quality of life. Optimization in radiotherapy is the primary step in the process of determining the optimal radiation doses for each patient. This process involves adjusting the intensity and direction of the beams in such a way that provides significant therapeutic benefits for the patient while simultaneously minimizing side effects. The optimization problem in this research is determining the optimal dose of radiation for the patient’s treatment. Optimization problems are converted into large linear systems, for which we use random linear algebra methods to solve. Randomized linear algebra methods are one of the efficient techniques in radiotherapy optimization and algorithms such as sketching, embedding, and others are used to solve optimization problems. Therefore, for solving various optimization problems like constrained or unconstrained least squares and others, random linear algebra methods are utilized. These methods reduce the dimensions of the original matrix and subsequently reduce the size of the linear system, which leads to faster problem-solving and reduced computational time. In the field of radiotherapy, this approach can improve the quality and accuracy of treatment, reduce time and treatment costs, and increase patient satisfaction by ensuring they receive the best therapeutic dose. In this thesis, we employ r andomized linear algebra techniques and algorithms such as decomposition, sketching, and dimensionality reduction, which are among the data (matrix) compression methods, with an emphasis on optimizing problems in radiotherapy using fewer computational resources and time, while maintaining acceptable accuracy comparable to the original problem. First, we review the basic concepts and principles of these techniques and randomized algorithms, and then examine the different implementation ideas of these algorithms and related models. Finally, based on the literature review, we implement an appropriate randomized linear algebra algorithm to analyze the error and execution time on the original matrix, and introduce the algorithm that has solved the optimization problems in less time and with acceptable accuracy
- Keywords:
- Embedded System ; Optimization ; Radiotherapy ; Least-Squares ; Cancer ; Scattering ; Randomized Linear Algebra Algorithms ; Random Optimal Dose ; Matrix Sketching
Digital Object List
-
محتواي کتاب
- view
Bookmark