Independent Component Analysis (ICA) has been developed as an efficient method to linearly transform input data to derive statistically independent components, and it has been recently used to derive the independent components of natural scenes. In this work, we study the influence of illuminant in the ICA results using as input sets of the same hyperspectral images under different daylight Spectral Power Distributions. Once the ICA bases were derived for each illuminant condition, we analysed the differences between them, and the reconstruction of color images with different bases and different number of basis functions. The results indicate that there are consistent differences between the bases corresponding to high and low solar elevations. The differences between atmospheric conditions are small for a given solar elevation. In the reconstruction results, the differences between original and reconstructed images with different ICA bases are more evident for the first 11 basis functions. With 61 basis functions, the results are rather similar for all the bases. We consider these results as a first step towards constructing an illuminant-invariant set of basis functions for color image representation.