The process for color restoration is very different from the “simple” white balance. In fact color balancing in general is very different from what’s usually described as white balancing (adjusting the color channels to ensure the brightest pixels in an image are white). Color balancing is the process of determining the colors of objects under white or neutral lighting conditions, for which there obviously is only one correct solution, namely the actual colors of the photographed or filmed objects under neutral lighting conditions. Color restoration essentially boils down to the same thing. This process is generally highly non-linear. You often don’t know what the colors should be or have a clearly defined gray point in an image. Therefore, although picking a white, gray, and black reference point will often give you a reasonable outcome, correcting very strong color casts caused by fading are beyond the capacities of such methods in my experience. However, the colors can be reconstructed, provided certain conditions are met. Take this example:

Original:

Simple white balance:

Automated color restoration:

The simple white balance removes the most obvious yellow cast, but does not remove it completely, and neither does it restore color.