This interdisciplinary work focuses on the interest of a new proximal algorithm (ADRS) for supervised classification of live cell populations growing in a thermostated imaging station and acquired by a Quantitative Phase Imaging (QP I) camera. This type of camera produces interferograms that have to be processed in order to extract features derived from quantitative linear retardance and birefringence measurements. We monitor cell cycling in different populations with both a classical fluorescent DNA intercalating agent imaging on the one hand and QP I without any cellular manipulation nor treatment on the other hand. We show that the accuracy of the classification of these cells in different phases of the cell cycle is equivalent, if not better, when using QP I features as compared to fluorescence imaging features. This is a very important finding since we demonstrate that it is now possible to very precisely follow cell growth under regular culture conditions without any bias. No dye or any kind of markers are necessary for this live monitoring, thus the cells normal physiology is not at all affected by this non invasive procedure. Any studies requiring analysis of cell growth or cellular response to any kind of treatment could benefit from this new approach..