Exploring Geometric Partial Differential Equations for Deep Learning and Image Processing
Bart Smets defended his PhD thesis cum laude at the Department of Mathematics and Computer Science on September 20th.
Image analysis is very important in various fields because it helps make critical decisions. Improving image analysis enhances decision-making and efficiency by providing more accurate and reliable results. This is crucial in areas like medicine, defense, and industrial automation, where precision and speed are essential. PhD researcher Bart Smets focuses on improving image analysis by combining two different methods: one based on mathematical equations (geometric partial differential equations) and the other based on artificial intelligence (deep learning). Smets successfully defended his PhD thesis with distinction on Friday, September 20th. As a result of his outstanding performance throughout his research, he was awarded his doctorate cum laude, signifying his high academic achievement.
Recently, deep learning has received a lot of attention for its ability to analyze images, but it has its own set of strengths and weaknesses. On the other hand, traditional methods based on mathematical equations also have their advantages and drawbacks.
' goal was to create a new method that combines the best features of both deep learning and mathematical approaches. This hybrid approach sought to overcome the limitations of using just one method, making it more effective for applications where either approach alone falls short.
Two lines of research
In his research, Smets focused on two lines of research. The first line of research explored combining traditional PDE-based image processing techniques with contemporary deep learning methods, while the second line investigated using total variation and mean curvature flows on SE(2) to enhance image denoising.
Smets introduced a new type of neural network architecture based on partial differential equations () that performed better than traditional convolutional neural networks, especially when there is limited data. This PDE-based approach reduced the number of parameters and enhanced the interpretability of the model.
Additionally, Smets' research explored the use of total variation and mean curvature flows on SE(2) for improving image denoising. These new denoising algorithms not only achieved better signal-to-noise ratios compared to popular methods like BM3D, but also preserved image edges more effectively. They were also robust to translation and rotation, providing consistent results even when the image was transformed.
Overall importance
Smets' research contributes to creating more efficient, interpretable, and reliable methods for tasks like image processing and denoising.
It addresses practical challenges such as limited data availability and ensures that results are robust across different conditions, making it potentially valuable for a wide range of applications.
Title of PhD thesis: . Supervisors: dr.ir. R. Duits, dr. J.W. Portegies
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