This paper proposes a new neural network structure for image processing whose convolutional layers, instead of using kernels with fixed coefficients, use space-variant coefficients. The adoption of this strategy allows the system to adapt its behavior according to the spatial characteristics of the input data. This type of layers performs, as we demonstrate, a non-linear transfer function. The features generated by these layers, compared to the ones generated by canonical CNN layers, are more complex and more suitable to fit to the local characteristics of the images. Networks composed by these non-linear layers offer performance comparable with or superior to the ones which use canonical Convolutional Networks, using fewer layers and a significantly lower number of features. Several applications of these newly conceived networks to classical image-processing problems are analyzed. In particular, we consider: Single-Image Super-Resolution (SISR), Edge-Preserving Smoothing (EPS), Noise Removal (NR), and JPEG artifacts removal (JAR).

中文翻译：

---

用于图像处理的非线性卷积网络

本文提出了一种新的图像处理神经网络结构，其卷积层不是使用固定系数的核，而是使用空间变量系数。采用这种策略可使系统根据输入数据的空间特征来调整其行为。如我们所展示的，这种类型的层执行非线性传递函数。与标准CNN层所生成的特征相比，这些层所生成的特征更加复杂，更适合于图像的局部特征。由这些非线性层组成的网络提供的性能与使用规范卷积网络的网络相当或更高，它们使用的层数更少，特征数量也大大减少。分析了这些新构想的网络在经典图像处理问题中的几种应用。特别是，我们考虑：单图像超分辨率（SISR），边缘保留平滑（EPS），噪声消除（NR）和JPEG伪像去除（JAR）。