For exact color reproduction of surfaces under various illuminants it is necessary to provide information on the complete reflectance spectrum. This work deals with the efficient representation of reflectance spectra. The number of values needed to represent a reflectance spectrum is reduced by linear transform coding of the spectra and by taking only a small number of transform coefficients. The aim is to find the basis functions for the linear transform such that an error criterion based on the perceptual color error difference is minimized. Depending on the error criterion different optimization schemes are employed and evaluated. The shape of the resulting basis function is analyzed and processed into a measure of roughness. This measure is then taken into account in the optimization, which results in smoother basis functions that lead to only a small degradation in the optimal color error values.