A Taylor expansion-based texture and edge-preserving interpolation approach for arbitrary-scale image super-resolution

The arbitrary-scale image super-resolution (ASISR) method based on implicit neural representation has exhibited remarkable performance. However, it struggles with texture and edge structure restoration, particularly at large upsample scales. This limitation arises from employing per-pixel L₁ loss exclusively and lacking constraints on image edge information within the upsample modules. To address this issue, we propose a novel texture and edge-preserving interpolation approach that leverages Taylor expansion within the upsample module for ASISR task and introduce a gradient loss, enabling better capture of subtle changes and edge structures. Leveraging the approximation capabilities of Taylor expansion, our approach improves the utilization of information of surrounding pixels for more accurate image restoration. In particular, we confine the space of the recovered images to the Bounded Variation space by the gradient loss, allowing functions to exhibit skip discontinuities (i.e., sharp edges of the image) while limiting the total variation. Then, we apply the Taylor expansion-based interpolation within this constrained space to achieve high-quality restored images. This approach maintains the overall smoothness of the images while effectively restoring the edges. Additionally, we introduce a Gradient-based Attention Block that can be seamlessly integrated into the standard Swin Transformer Layer to capture high-frequency information within features. Experimental results demonstrate that our interpolation approach significantly enhances the recovery of edge structure information and texture in SR images, outperforming previous state-of-the-art methods, especially on Urban100 and Manga109 datasets, which have complex line structures and texture details. Our code is available at https://github.com/boohit/Taylor-Expansion-based-EIUM.