Ringing artifacts

[CptPotato]

I'm getting some ringing artifacts with tony, especially noticeable in light grey gradients:

right side with increased contrast

At first I thought that I integrated the tone mapper incorrectly, but it seems like these artifacts are part of the LUT. If I pass a neutral LUT to the tone mapping shader, the artifacts are gone.

As a (very) crude workaround I refitted the LUT to an approximate luminance, which gets rid of the ringing but changes the tone mapper's look a bit:

Edit: The workaround turned out to be quite off on highly saturated colors.

_{PS: thanks for sharing this neat tone mapper}