A multi-scale analyzing tool is now available to investigate the temporal evolution of two phase flows such as liquid systems experiencing an atomization process. Thanks to its multi-scale and global nature, it allows identifying all dynamics simultaneously involved in the process with no restriction of the liquid system shape. In the present work this multi-scale tool is applied on 2D visualizations of free falling jets of a low-viscosity viscoelastic solution. The jets are produced from a cylindrical discharge orifice and the liquid is a very dilute polymer solution containing 5 ppm of Poly(ethylene oxide). High spatial resolution images of the free falling jets are performed as a function of the velocity and at several distances from the discharge orifice. For every operating condition, the liquid jet remains cylindrical first, then shows the development of a sinusoidal perturbation and finally adopts a beads-on-a-string pattern before breakup occurs. The multi-scale analysis is performed on a high number of images and at several spatial positions in order to return statistical and temporal information, respectively. The results of this analysis show that during the sinusoidal perturbation stage, the large-scale region follows an exponential increase as predicted by the linear stability theory and during the beads-on-a-string stage, the small-scale region follows an exponential decrease similar to an elasto-capillary regime from which the relaxation time of the polymer solution can be extracted. This work positions the multi-scale approach as a promising and complementary tool to the currently used techniques in order to probe complex liquid rheology, especially in the case of mobile viscoelastic solutions.