Determining what filter (if any) has been applied to an image I'm trying to determine what "filter" has been applied to an image.  I have the original, raw image and the processed image.  The processed image has been put through a pipeline (black box) that does various things to the image in an iterative manner.

The filter, as far as I can tell, is similar to an unsharp-mask, but with "negative bowls" mitigated.  However, the processed image cannot be reproduced by a simple unsharp mask.

I've attempted to measure the "filter function" by taking the ratio of the power spectra of the raw and unprocessed images, but the best I've been able to do with that is unsharp mask with a non-gaussian smoothing function.

What methods are available for determining the filter applied to an image?

(not related to Determining the type of filter on an image)
In case your filter is linear, this should be quite easy. You have a linear model with unknown parameters (9 if your support is 3x3, 16 if 4x4, etc...). You have a lot of constraints - the original image and result image. You can use linear least squares. If you can generate any input, it is even easier. Recall that a linear time-invariant system is fully determined by its response to delta impulse, which is its kernel.
In case your filter is not linear (like Paul says), there is almost nothing that you can do to find it out, except using your common sense, or attempting to optimize another model, given your inputs and outputs. Image processing logic can be very non-linear, including ad-hoc solutions, so it looks quite hard to me.