I have a raster graphic consisting of a solid-black icon with anti-aliased edges on top of a shaded-red background. I also have the background alone, without the icon on top. Is it possible to recover the solid-black icon alone, without the background (i.e. get the solid-black icon with its anti-aliased edges on a pure-white or transparent background)?
I tried various combinations of Photoshop blend modes and filters, but nothing worked perfectly. I think the problem is that the background is shaded instead of being a solid color. For example, using the "Difference" blend mode converts the image from solid-black-icon-on-shaded-red-background to shaded-red-icon-on-solid-black-background. Converting that to grayscale and inverting the color produces a shaded-gray icon on a pure-white background. Adding a "Curves" filter on top allows me to bring portions of the icon down to pure-black, but no matter how I fiddle with it, the result doesn't perfectly match the original when I layer the isolated icon back on top of the isolated background — the anti-aliased edges are always slightly off.
The icon with background (blown up to 800% with Nearest-Neighbor interpolation to be more visible):
The background on its own (blown up to 800% with Nearest-Neighbor interpolation to be more visible):