Using ordinary digital cameras as relatively cheap measurementdevices for estimating spectral color properties has becomean interesting alternative to making pointwise high precisionspectral measurements with special equipments like photospectrometers.The results obtained with these methods cannotcompete with the quality of the traditional high resolutiondevices but they are very attractive since the equipment is relativelycheap and instant measurements are obtained for millionsof measurement points.In this paper we investigate the problem of estimating reflectancespectra from measurements taken with ordinary digitalRGB cameras. We study the effects of using multiple illuminationsand treat the estimation of the reflectance spectra asa regression or a statistical inversion problem. We use both,linear- and non-linear estimation methods where we focus onusing reproducing kernels to avoid explicit formulation of nonlinearities.We also include non-linear conditions based on theproperties of the reflection spectra. Munsell Matte color andPantone are used as data sets to support the proposed methods.The experiments show that the proposed methods improve the estimationresults when compared to standard linear methods.