You cannot do that.
Pure blue can be composed from the blue color plane with no red or green.
Pure yellow can be composed from the blue color plane together with equal amounts of red, with no green.
If we restrict ourselves to the easier case of each pixel being either pure blue or pure yellow, then we restrict ourselves to the forms
(0, 0, b) %pure blue
(c, c, 0) %pure yellow
RGB converts to gray with the formula 0.2989 * R + 0.5870 * G + 0.1140 * B so we get
gray1 = 0.1140 * b
gray2 = 0.2989 * c + 0.5870 * c + 0.1140 * 0 = 0.8859 * c
Can they equal each other?
0.1140 * b = 0.8859 * c
b = 0.8859/0.1140 * c = 7.771 * c
and if we are using uint8, then to within the rounding that is automatically done, this means that
(0, 0, 7)
has the same brightness as
(1, 1, 0)
There are grayscale intensities that could be produced by either a pure blue or a pure yellow and they cannot be distinguished. Therefore you cannot reliably map from grayscale intensity back to pure blue vs pure yellow.
The problem gets much much worse if you permit shades of color.
