Estimation of the diffusion propagator from a sparse set of diffusion MRI (dMRI) measurements is a field of active research. Sparse reconstruction methods propose to reduce scan time and are particularly suitable for scanning un-coperative patients. Recent work on reconstructing the diffusion signal from very few measurements using compressed sensing based techniques has focussed on propagator (or signal) estimation at each voxel independently. However, the goal of many neuroscience studies is to use tractography to study the pathology in white matter fiber tracts. Thus, in this work, we propose a joint framework for robust estimation of the diffusion propagator from sparse measurements while simultaneously tracing the white matter tracts. We propose to use a novel multi-tensor model of diffusion which incorporates the biexponential radial decay of the signal. Our preliminary results on in-vivo data show that the proposed method produces consistent and reliable fiber tracts from very few gradient directions while simultaneously estimating the bi-exponential decay of the diffusion propagator.