Some of the answers here discussed a more complex question:
what is the optimal mapping of more than 4 colors into a 3 component image.
This is a very subjective question. From an artistic standpoint, there is no good answer.
But from an engineering standpoint, one can use compression algorithms. A very basic algorithm for multiple band compression is called PCA (principal component analysis).
It 'basically' finds a linear transformation of your X spectral components into Y new spectral components in a way that:
- each component is orthogonal to the other (they have minimal correlation).
- the components are sorted by the level of variability in the image. so the first components have most of the data and the last components are mostly noise.
so basically using an algorithm such as PCA or equivalent and displaying the first 3 components as your RGB would give you an image with maximum information and contrast that can be put into a 3 band composition. Is it going to be a pretty image? not necessarily. natural looking? most probably no. But its probably more useful if you were a scientist/engineer and wanted to improve contrast.