In the latest years, multifractal analysis has been applied to image analysis. The multifractal framework takes advantage of multiscaling properties of images to decompose them as a collection of different fractal components, each one associated to a singularity exponent (an exponent characterizing the way in which that part of the image evolves under changes in scale). One of those components, characterized by the least possible exponent, seems to be the most informative about the whole image. Very recently it has been proposed an algorithm to reconstruct the image from this component, just using physical information conveyed by it. In this paper, we will show that the same algorithm can be used to assess the relevance of the other fractal parts of the image.