  Inspired by the traditional partial differential equation (PDE) approach for
image denoising, we propose a novel neural network architecture, referred as
NODE-ImgNet, that combines neural ordinary differential equations (NODEs) with
convolutional neural network (CNN) blocks. NODE-ImgNet is intrinsically a PDE
model, where the dynamic system is learned implicitly without the explicit
specification of the PDE. This naturally circumvents the typical issues
associated with introducing artifacts during the learning process. By invoking
such a NODE structure, which can also be viewed as a continuous variant of a
residual network (ResNet) and inherits its advantage in image denoising, our
model achieves enhanced accuracy and parameter efficiency. In particular, our
model exhibits consistent effectiveness in different scenarios, including
denoising gray and color images perturbed by Gaussian noise, as well as
real-noisy images, and demonstrates superiority in learning from small image
datasets.
