Machine Learning And Its Application In Inverse Problems
Inverse problems have wide applications covering from the medical imaging in our daily lives to studying our solar system dynamics and beyond. In contrast to direct problems trying to find the effect from cause, inverse problems aim to determine the cause from given results. A typical example of inverse problems in medical imaging is X-ray tomography. This tomography relies on collections of X-ray projection images of a physical body, from which one applies an inverse problem technique to reconstruct the body’s inner structure. This would help doctors predict the patient’s situation and give a precise diagnosis. In this project, we focus on studying the mathematics behind X-ray tomography, and also utilize convolutional neural networks to reconstruct the Shepp-Logan phantom. The outcome is compared the reconstruction by learned gradient descent scheme using convolutional neural networks with different layers.