Colors in many paintings of great art historical value have changed over time, due to the combined effects of natural ageing, accumulated surface grime, and materials added during later conservation treatments. The physical restoration of the colors in such paintings is not possible. This article describes one part of work done to digitally restore the colors of Van Gogh's painting Field with Irises near Arles, dating from May 1888. We have used multispectral reflectance data to estimate absorption K and backscattering S parameters of Kubelka-Munk 2-constant theory. This was done for all 13 pigments known to have been used by Van Gogh in this painting, and based on this the concentration maps for each of these pigments were calculated. We validated the calculated concentration maps in several ways. For some pigments, we were able to predict spots on the painting where the pigment is expected to occur in unmixed form based on visual examination. For several other pigments, the concentration maps could be shown to agree with XRF data. Finally, for some other pigments the concentration maps were supported by additional evidence from microscopic examinations, remarks in Van Gogh's letters and from early color reproductions. For the 1.7 million pixels for which multispectral data is available, the average color difference between the calculated and measured spectral reflectance curves is CIEDE2000 = 1.05. This further confirms that the Kubelka-Munk calculations are well suited to describe the variety of spectral reflectance on the painting.