Help with uneven fading

The two main goals here are:

1. Isolate the region that’s differently faded.

2. Reverse the fading to match the other region. 

#1 is addressed with a mask. Because the faded area is an oval, it’s easy to match that using a mask drawn with the Elliptical Marquee tool or Ellipse tool.

#2 is easier if you understand why the area inside the oval mat faded. It was because of dyes in the photo print fading at uneven rates over many years. Light fades the yellow dye first (which is why the image shifted toward blue), then the cyan (which is why the image also shifts toward red), and finally the magenta dye. You can apply knowledge about dye fading to try and reverse it manually using Curves or Levels adjustments.

I gave it a quick try, as shown in the demo below. I found that the oval is slightly rotated, probably because the photo was put behind the mat slightly rotated.

My solution uses a single Curves adjustment layer with an elliptical vector mask. The mask hides edits outside the ellipse I drew. In the Properties panel for the Curves adjustment layer, edits are made to each of the curves (luminance, and the Red, Green, and Blue channels) until the colors inside the ellipse match the colors outside the ellipse.

It isn’t perfect, because it looks like there the fading also varied from top to bottom. For example, the color of the hands looks OK but the face is too green. That could be addressed with another adjustment layer with a gradient mask applied to it to control how the correction varies across the image.

I used two pairs of Eyedropper tool color samplers to report the color values at two different levels inside and outside the ellipse. As I edit curves, watching these values change in the Info panel helps to understand which way to drag the points. (Monitoring the per-channel color values is a traditional method that goes back decades.)

There are also two more things to be done, which I did not go on to do. After matching up the colors, the overall color balance is unnatural so that still needs to be corrected. It would also be a good idea to add one last empty layer on top, then on that layer, drag the Spot Healing Brush tool set to Sample All Layers over the visible mat border and any scratches or other damage, to repair them.

This method uses no AI, but there’s nothing wrong with trying to fix the damage with Generative Fill as Trevor did, and the Remove tool if you run into something the Spot Healing Brush tool can’t handle.

This was a bit left field, but it seems to have worked.

I carefully selected the oval by using the elliptical Marquee tool and Transform Selection.

I inverted the selection and expanded it by 5 pixels so that I had all of the darker outer area selected.

And used Generative Fill with no prompt.

This was the best of the three options.  It needs some touching up, but the tones are reasonably close across the image.

Ooo, those are fun restorations, James. Many ways to flay the feline. A few abreviated ideas:

(selecting the layer easily is tricky)

Promote the faded area to a new layer, then

Image>Adjustments>Match Color, adjust sliders Luminance and Color Intensity

-or-

Promote the faded area to a new layer, then eyeball to match, if your vision is up to it

-or-

Fake it - selected the faded area, invert the selection, feather the selection, lower Exposure

One could also try the beta Photo Restoration Neural Filter; or Camera Raw masking of faded area, eyeballing manipulation.

Let's hope a restoration magician has better ideas, James!