•  Yoseob Han and Jong Chul Ye,"Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT", Special Issue on Machine Learning for Image Reconstruction, IEEE Trans. on Medical Imaging (in press),  2018. ​

  X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient  projection views, an analytic  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. 
Inspired by the recent theory of  {\em deep convolutional framelets},  the main goal of this paper is, therefore, to  reveal the 
limitation of U-Net and propose new multi-resolution deep learning schemes. In particular, we show that the alternative U-Net variants such as dual frame and  the tight frame U-Nets satisfy the so-called frame condition which make them better for effective recovery of high frequency edges in sparse view-CT.  Using extensive experiments with  real patient data set, we demonstrate that the new network architectures provide  better reconstruction performance.

• Eunhee Kang, Won Chang, Jaejun Yoo, and Jong Chul Ye, "Deep Convolutional Framelet Denosing for Low-Dose CT via Wavelet Residual Network", Special Issue on Machine Learning for Image Reconstruction, IEEE Trans. on Medical Imaging (in press),  2018.

Model based iterative reconstruction (MBIR) algorithms for low-dose X-ray CT are computationally expensive. To address this problem, we recently  proposed a deep convolutional neural network (CNN) for low-dose X-ray CT and won the second place in 2016 AAPM Low-Dose CT Grand Challenge. However, some of the texture were not fully recovered.  To address this problem, here we propose a novel  framelet-based denoising algorithm using wavelet residual network  which synergistically combines the expressive power of deep learning and the performance guarantee from the framelet-based denoising algorithms.  The new algorithms were inspired by the recent interpretation of the deep convolutional neural network (CNN) as a cascaded convolution framelet signal representation. Extensive experimental results confirm that the proposed networks have significantly improved  performance and preserves the detail texture of the original images.

• Dongwook Lee, Jaejun Yoo, Sungho Tak and Jong Chul Ye, "Deep Residual Learning for Accelerated MRI using Magnitude and Phase Networks", IEEE Trans on Biomedical Engineering (in press), Invited Paper for Special Section on Deep Learning, 2018.

Accelerated magnetic resonance (MR) scan acquisition  with compressed sensing (CS) and parallel imaging  is a powerful method to reduce MR imaging scan time. However, many reconstruction algorithms have high computational costs.  To address this, we investigate  deep residual learning networks to remove aliasing artifacts from artifact corrupted images. The deep residual learning networks are composed of magnitude and phase networks  that are separately trained. If both phase and magnitude information are available, the proposed algorithm can work as an iterative  k-space interpolation algorithm using framelet representation.  When  only magnitude data is available, the proposed approach works as an image domain post-processing algorithm. We provide the underlying mathematics to optimize the network structure using recent deep convolutional framelets theory. Comparisons using single and multiple coil show that the proposed residual network provides good reconstruction results with orders of magnitude faster computational time than existing compressed sensing methods.