Photoshop mapping colors

Question

I have a colored image with gradients that got color-distorted. By distorted, I mean that the colors have been shifted (not in a linear way) but in a global way, not locally.
I know exactly which parts of the image should have which colors but since there are complicated gradients involved it's not so easy to just replace a color. Using adjustments layer like color balance is also not very helpful, because it's difficult to set the sliders exactly the way I want and there may be no combination at all that changes all the colors the way I want them to be.

Is there a way to tell Photoshop directly which input color should map to which output color and blend the rest accordingly? E.g. if I tell PS that red should map to yellow and orange should map to green then an orangy-red should map to a yellowish-green.

Edit (Example):

This is part of a scan that I'm working with. It's unedited apart from rotating, skewing and resizing.

There are 3 types of gradients: a simple linear gradient for the hair, a more complicated gradient for the skin (it's hard to see, it will have to be enhanced greatly) and wherever two colors meet.
First, I get rid of the noise and grain. I do this by using a smart blur filter and a great deal of manual clean up. There may be a more efficient method but that is not the main point of the question.
Next, the colors of the scan are all wrong. Since they are mostly flat colors I tried to select them with color range and fill the selections with the intended color or apply a color adjustment layer for this selection only.
However, that leaves the areas anywhere two or more colors meet and mix into each other. I don't know how to account for this and that's what I meant with complicated gradients. Making exact selections of the colored areas is really tricky and blurring it makes the image much too blurry (no surprise).

Answer 1

Your image has a moire-like repeating pattern. I assume that you called it "the noise" . If one scans a printed image, a pattern of same type appears. But that doesn't cause global color errors.

The "noise" can be greatly reduced in a good noise eliminating program that is smart enough to leave the edges as non-blurred.

I tried "Open as Camera RAW" to have its noise reduction available. The reduction was remarkable. See the screenshot:

If you add the "Clarity" you can make all strokes stronger, even nearly black. That does not bring the noise back. It's not used above.

A noise sample based program "Neat Image" also did the job. The noise sample must be taken from a large area that has a single flat color. In your image there were only few areas large enough.

You can try correct the gradients by using Image > Adjustments > Hue/Saturation. It can change all colors or a narrow color range. Here it's used to all colors. The adjustment has only one objective: Correct the skin color:

In theory you can get a bunch of layers that all have mostly false colors, but one color is fixed. Then you somehow erase from all layers everything, but the fixed color and be happy of the totally fixed appearance.

Theoretically by using the Hue/Saturation to a narrowed color range, you can fix to one layer several colors and radically reduce the erasing work.

Another theoretical possiblity in Photoshop:

Let's call your image =A. Create version B where a substantial amount of areas are corrected manually. Have a saved selection that covers exactly the corrected areas. Activate the same selection in both A and B. Then use Photoshop's Match Color. Have the correction based on the selection, but extended to whole images. The selection can be collected bit by bit into an empty layer in B, where an area is painted with a solid color as soon as an area is corrected in the image layer. Finally copy that layer into A and select all non-transparent by the magic wand. I have tried this only in much less complex cases, where no criss-crossings over the color wheel were not needed.

Seriously: If only your scanning system is down and no fix is available, but you have the image, take a photo of it. A good photo is not impossible. Take it as a RAW for best adjustability and to be able to fix the white balance easily. If raw is not available, open the JPG as Camera Raw in Photoshop.

Answer 2

It would seem the real solution to your problem is perhaps to address why the scanner isn't working properly. To replace it or borrow a working one would seem to be the obvious answer. Taking a photograph of the artwork is also possible.

In the meantime, to address your actual question, it is possible to use the Select > Color Range option to make selections before applying Hue/Saturation adjustment layers to alter the colours of different parts of the image selectively. It's also possible to adjust the fuzziness of the tool to help select the gradients.

Once you have targeted the colours that need changing, you can further refine the layer masks by simply painting on them in black where you don't want the Hue/Saturation to change.

See example here of the kind of thing that is possible.

Your secondary issue regarding the noise (which is actually the half-tone pattern of a print, and not in fact noise) can be solved by converting the artwork to a Smart Object, and by using the Camera RAW filter to apply noise reduction.