The MARS (Medipix All Resolution System) research group is developing a CT (Computed Tomography) scanner which uses the Medipix range of energy discriminating photon counting detectors. These detectors have the potential to significantly improve the functionality of medical scanners and reduce patient radiation exposure. An image processing technique that benefits from this type of detector is material decomposition. The goal of material decomposition is to take data obtained at different energies and produce material density maps of each material in the scanned region. This project contains the start of preliminary investigations into using compressive sensing as a method for material decomposition in the MARS Spectral CT Scanner system. L1 - Minimization methods from the YALL1 open source l1 optimization package are currently being tested on phantom data representing 7 different medically relevant materials - Air, vVater, Perspex, Calcium, Iron, Iodine and Fat. Calcium, Iron, Iodine and Fat were expressed in the phantom by the compounds Calcium Chloride (aq) [2M], Ferric Nitrate (aq) [0.4M], Iodine (aq) [0.02M] and Sunflower Oil. More results are needed to draw firm conclusions about the viability of this method, however initial results on simulated data shown in this report are promising.