Image Interpolation Using the Yule Walker Equations
The main problem is Auto Regressive (AR) / IIR models are based on the idea of something before and after.
While for time series it is well defined, how will you address that in image for a pixel in the middle of the image?

I addressed some ideas on that in my answer to the question Denoising an Image Using Kalman Filter.

Another idea is to work across rows and then across columns.
Then you can build an AR model based on the samples with unit "Time Parameter" and then ask what should happen for $ n / 2 $ or so.
You can even take it farther, and in order to use the 2D information take $ k $ rows / columns at a time and build a vectorized AR model.
Then it means that for each pixel you'll get $ k $ estimations which you could average or chose any other idea to fuse.

Actually it could be nice idea to have a try...