On comparison of learned reconstructions in supervised and unsupervised training settings with Noise2Inverse

Abstract

In this thesis the aim is to extend a learned reconstruction algorithm called Learned Primal Dual to be unsupervised with a method called Noise2Inverse. Results are compared to supervisedly trained networks and to the classical reconstruction algorithms.

Reconstructing the CT-image from the CT-scan data is not straight forward and it can be seen as an inverse problem. This thesis gives a broad information on background knowledge and how this inverse problem can be solved with both classical and modern reconstruction algorithms.

First the thesis focuses on the basic and necessary theory of the CT-imaging, as it goes through a Radon and X-ray transforms, and gives a mathematical expressions on how different CT-scan geometries work. Also the consept of linear inverse problems is introduced and theory on regularization and variational methods is brought in. With the help of regularization and variational methods, two classical reconstruction methods are introduced and their results are compared and discussed.

Second the thesis focuses on the modern part of solving the inverse problem in question. The modern solving methods in this thesis mean a ones that adapt neural networks to increase the solving quality. There is a section that goes through an information about deep learning and the most important subsection being the one about convolutional neural networks.

After the deep learning part the learned reconstruction algorithms are introduced and three different algorithms are being looked at. Those algorithms are the U-Net, the Learned Gradient Scheme and the Learned Primal Dual. These all are build with convolutional neural networks. Results on these algorithms trained with the supervised setting are shown and compared to each other as well as to the classical ones.

Finally the unsupervised training settings are introduced with main focus on Noise2Inverse method. There is shown that the Noise2Inverse method can be applied to the Learned Primal Dual algorithm and the results are compared to the Noise2Inverse applied to the U-Net as well as to the same algorithms that were trained supervised.