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.

翻译：受传统偏微分方程（PDE）图像去噪方法的启发，我们提出了一种新颖的神经网络架构——NODE-ImgNet，该架构将神经常微分方程（NODEs）与卷积神经网络（CNN）模块相结合。NODE-ImgNet本质上是一个PDE模型，其动态系统以隐式方式学习，无需显式指定PDE形式，从而自然规避了学习过程中引入伪影的典型问题。通过采用这种可视为残差网络（ResNet）连续变体并继承其在图像去噪中优势的NODE结构，我们的模型实现了更高的精度和参数效率。特别地，该模型在不同场景下均展现出稳定有效性，包括对受高斯噪声干扰的灰度与彩色图像去噪以及真实噪声图像处理，并在小样本图像数据集学习中表现出优越性能。