Recent approaches for arbitrary-scale single image super-resolution (ASSR) have used local neural fields to represent continuous signals that can be sampled at different rates. However, in such formulation, the point-wise query of field values does not naturally match the point spread function (PSF) of a given pixel. In this work we present a novel way to design neural fields such that points can be queried with a Gaussian PSF, which serves as anti-aliasing when moving across resolutions for ASSR. We achieve this using a novel activation function derived from Fourier theory and the heat equation. This comes at no additional cost: querying a point with a Gaussian PSF in our framework does not affect computational cost, unlike filtering in the image domain. Coupled with a hypernetwork, our method not only provides theoretically guaranteed anti-aliasing, but also sets a new bar for ASSR while also being more parameter-efficient than previous methods.

翻译：近期针对任意尺度单图像超分辨率（ASSR）的方法采用局部神经场来表示可在不同采样率下采样的连续信号。然而在此类框架中，对场值的逐点查询与给定像素的点扩散函数（PSF）存在天然不匹配。本文提出一种新型神经场设计方法，使得查询点可关联高斯PSF——该函数在跨分辨率移动时作为抗混叠滤波器用于ASSR。我们通过基于傅里叶理论及热传导方程推导的新型激活函数实现该特性，且不增加额外计算成本：与图像域滤波不同，本框架中采用高斯PSF查询点不会影响计算量。结合超网络，本方法不仅提供具有理论保证的抗混叠效果，更在参数效率超越既往方法的同时，为ASSR树立了新标杆。