Thierry Blu

Shutian Zhao, Donal G. Cahill, Siyue Li et al.

Two-dimensional (2D) fast spin echo (FSE) techniques play a central role in the clinical magnetic resonance imaging (MRI) of knee joints. Moreover, three-dimensional (3D) FSE provides high-isotropic-resolution magnetic resonance (MR) images of knee joints, but it has a reduced signal-to-noise ratio compared to 2D FSE. Deep-learning denoising methods are a promising approach for denoising MR images, but they are often trained using synthetic noise due to challenges in obtaining true noise distributions for MR images. In this study, inherent true noise information from 2-NEX acquisition was used to develop a deep-learning model based on residual learning of convolutional neural network (CNN), and this model was used to suppress the noise in 3D FSE MR images of knee joints. The proposed CNN used two-step residual learning over parallel transporting and residual blocks and was designed to comprehensively learn real noise features from 2-NEX training data. The results of an ablation study validated the network design. The new method achieved improved denoising performance of 3D FSE knee MR images compared with current state-of-the-art methods, based on the peak signal-to-noise ratio and structural similarity index measure. The improved image quality after denoising using the new method was verified by radiological evaluation. A deep CNN using the inherent spatial-varying noise information in 2-NEX acquisitions was developed. This method showed promise for clinical MRI assessments of the knee, and has potential applications for the assessment of other anatomical structures.

Zikai Sun, Thierry Blu

The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately limiting their generalization performance. To address this limitation, we devise a method that endows CNNs with simultaneous equivariance with respect to translation, rotation, and scaling. Our approach defines a convolution-like operation and ensures equivariance based on our proposed scalable Fourier-Argand representation. The method maintains similar efficiency as a traditional network and hardly introduces any additional learnable parameters, since it does not face the computational issue that often occurs in group-convolution operators. We validate the efficacy of our approach in the image classification task, demonstrating its robustness and the generalization ability to both scaled and rotated inputs.