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Master Thesis: Solving the Forward and Inverse Problem of the 2D-Helmholtz Equation using a Convolutional Neural Network
This thesis is part of an interdisciplinary project called Minimally Invasive Robot-Assisted Computer-guided LaserosteotomE (MIRACLE) from the Department of Biomedical Engineering at the University of Basel. The goal of this project is to develop a minimally invasive robotic endoscope to cut bones with laser-light.
During tissue ablation with laser-light, an acoustic wave is emitted (Kenhagho et al., 2018).
By measuring these emitted waves, the characteristic speed of sound in different tissue types allows for an inference of the surrounding tissue type.
However, the classical numerical approaches to do so (Nahum et al., 2019) are time-consuming and not yet suitable for a real-time feedback system.
Hence, we want to improve the computational time of our simulation of the Helmholtz equation using a Convolutional Neural Network (CNN).
During tissue ablation with laser-light, an acoustic wave is emitted (Kenhagho et al., 2018). By measuring these emitted waves, the characteristic speed of sound in different tissue types allows for an inference of the surrounding tissue type. However, the classical numerical approaches to do so (Nahum et al., 2019) are time-consuming and not yet suitable for a real-time feedback system. Hence, we want to improve the computational time of our simulation of the Helmholtz equation using a Convolutional Neural Network (CNN).
The goal of this thesis is to simulate the behavior of sound waves for inference of the underlying tissue using a CNN.
You will learn the basics of solving partial differential equations with finite elements to numerically compute a sound wave given by the Helmholtz equation, solving the so-called forward problem.
You will use the resulting simulations as ground truth data to train a CNN, which may then be used to speed up the computations considerably.
In a final step, you reconstruct the structure of a simulated 2D bone - also known as solving the inverse problem - in an increasingly realistic setup.
The goal of this thesis is to simulate the behavior of sound waves for inference of the underlying tissue using a CNN. You will learn the basics of solving partial differential equations with finite elements to numerically compute a sound wave given by the Helmholtz equation, solving the so-called forward problem. You will use the resulting simulations as ground truth data to train a CNN, which may then be used to speed up the computations considerably. In a final step, you reconstruct the structure of a simulated 2D bone - also known as solving the inverse problem - in an increasingly realistic setup.