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 the 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, westudy the X-ray tomography by utilizing machine learning technique. The Shepp-Logan phantom, serves as the model of a human head, is reconstructed from simulated data by using the learned gradient descent. The outcome is compared against different traditional reconstruction methods, including Tikhonov Regularization and Total Variation regularization. Finally, we discuss the performance of these reconstruction methods.