Periodic Features for CNNS in JPEG artefact removal

Okay, so this is just a note for an idea for a CNN architecture for JPEG artefact removal, improving on the vanilla Dong-esque method.

The use of convolutional neural networks in the context of low-level vision, such as denoising, demosaicing, artefact removal or superresolution is motivated by the following two assumptions:

\item[Locality:] We assume that to recover the value of an output pixel, it is sufficient to integrate information from a local neighbourhood around the corresponding location in the input image
\item[Translational equivariance:] We assume that the operation we apply to recover a pixel should be largely the same across different locations within the image, so the same input patch but in a translated position should generate the same output patch.

Convolutional networks allow us to exploit these two assumptions of locality and translational equivariance, whilst retaining great flexibility and expressive power within these constraints.

Crucially, in certain applications such as superresolution and JPEG artefact removal, we want a milder form of translational equivariance. Instead of requiring full translational equivariance in the output pixels, we only want equivariance to translations that are a multiple of some block size $r$. In superresolution $r$ is the upsampling ratio