> And there are multiple ways with completely different combinations of intesities of light at different frequencies to have a color that most people will see as the same color. This is because the color receptors of our eye overlap.

Of course, if you read back you will notice I am quite aware that the mapping is not a one to one bijection. Hence the need to solve the inverse problem.

One can maintains the inverse image (a set), or maintain a distribution over that, or certain statistics of that distribution. I have a link in my post about what inverse problems are.