Dual energy x-ray computed tomography (DECT) is a valuable research tool for both clinical and preclinical studies and a field of extensive research. Current implementations of DECT rely on the acquisition of two datasets either by using two source-detector pairs or by rapidly switching the kVp of the x-ray source between consecutive projections. Both alternatives require specific hardware, only available in a small number of systems. DECT data can also be acquired using standard hardware and minimizing acquisition time and dose by slowly modulating the kVp of the source to obtain the whole dataset in a single rotation. However, in this case, highly undersampled, non-registered data are obtained for the high and low-energy sinograms, depending on the slew rate used for the kVp modulation. We propose a novel iterative method for raw data DECT material decomposition for slow modulation kVp by using a compressed sensing approach. Information provided by the slow switching kVp data at intermediate kVp values is used to generate a prior term containing the edges of the different regions in the sample. The problem is efficiently solved by the use of the Split-Bregman method. Preliminary experiments on simulated data show promising results for the decomposition of slow modulated kVp DECT data into two material basis sinograms, obtaining acceptable error in the decomposed dataset from highly undersampled data.