The multispectral acquisition of frescoes poses unsolved challenges, the main difficulty being that it is often impossible to measure the reference white signal. We introduce a new formulation of the lightness problem for images of pictorial artworks. As artists often paint the effects of light, the albedo field can contain a component that mimics an illumination field. Therefore, new insights are needed to distinguish the effects of physical illumination and painted shading. Because paint has a small dynamic range compared to light, these two signals can be distinguished using dynamic range. We describe a variational method to estimate the physical illumination component. We show our method produces estimates of the illumination intensity field for multispectral images of paintings that compare very well with the known ground truth, outperforming other state-ofthe art lightness recovery algorithms. We then apply our method to a fresco for which the reference white signal had not been acquired. We propose a definition of consistency for lightness recovery algorithms, and show our method satisfies it fairly well.