Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT

X-ray computed tomography (CT) using sparse projection views is often used to reduce the radiation dose. However, due to the insufficient projection views, a reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-net have demonstrated impressive performance for sparse view CT reconstruction. However, theoretical justification is still lacking. The main goal of this paper is, therefore, to develop a mathematical theory and to discuss how to improve these algortihms. In particular, inspired by the recent theory of deep convolutional framelets, we show that the U-net relies on a sub-optimal nonlocal bases that overly emphasizes low frequency components. The discovery leads to a dual frame and a tight frame Unet architectures for effective recovery of directional image components.