Inverse problems arise in a wide variety of applications including biomedicine, environmental sciences, astronomy, and more. Computing reliable solutions to these problems requires the inclusion of prior knowledge in a process that is often referred to as regularization. Most regularization techniques require suitable choices of regularization parameters. In this work, we will describe new approaches that use deep neural networks (DNN) to estimate these regularization parameters. We will train multiple networks to approximate mappings from observation data to individual regularization parameters in a supervised learning approach. Once the networks are trained, we can efficiently compute regularization parameters for newly-obtained data by forward propagation through the DNNs. The network-obtained regularization parameters can be computed more efficiently and may even lead to more accurate solutions compared to existing regularization parameter selection methods. Numerical results for tomography demonstrate the potential benefits of using DNNs to learn regularization parameters. / Master of Science / Inverse problems arise in a wide variety of applications including biomedicine, environmental sciences, astronomy, and more. With these types of problems, the goal is to reconstruct an approximation of the original input when we can only observe the output. However, the output often includes some sort of noise or error, which means that computing reliable solutions to these problems is difficult. In order to combat this problem, we can include prior knowledge about the solution in a process that is often referred to as regularization. Most regularization techniques require suitable choices of regularization parameters. In this work, we will describe new approaches that use deep neural networks (DNN) to obtain these parameters. We will train multiple networks to approximate mappings from observation data to individual regularization parameters in a supervised learning approach. Once the networks are trained, we can efficiently compute regularization parameters for newly-obtained data by forward propagation through the DNNs. The network-obtained regularization parameters can be computed more efficiently and may even lead to more accurate solutions compared to existing regularization parameter selection methods. Numerical results for tomography demonstrate the potential of using DNNs to learn regularization parameters.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/114978 |
| Date | 08 May 2023 |
| Creators | McDonald, Ashlyn Grace |
| Contributors | Mathematics, Gugercin, Serkan, Arnold, Rachel Florence, Chung, Julianne |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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