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.

利用傅立叶理论和热方程衍生的一种新型激活函数，我们提出了一种设计神经场的新方法，使得可以使用高斯点扩散函数查询点，在 ASSR 分辨率转换时提供了理论上保证的抗锯齿效果，并且在计算成本上不增加额外开销，同时与超网络结合，比之前的方法更具参数效率。