If "art is in the eye of the beholder," then an artistic decomposition would provide inconsistent results across populations. It seems more important that the data decompose in a more repeatable and reliable way.
Idea: create a transmission format which creates specific artifacts only in the presence of certain types of interference or failure modes. The format would likely need to created on a situational basis. It seems likely that this has been created, but I've never heard of something like it.
>Is there an encoding that would naturally produce smoothed visuals without sufficient data?
You might enjoy the results of wavelet compression [1]. An image format using wavelet compression is JPEG2000 [2].
[1] https://image.slidesharecdn.com/sjbit-ncp-2013-140401124704-... [2] https://en.wikipedia.org/wiki/Wavelet_transform#Wavelet_comp...