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).
