Diffusion Weighted Imaging (DWI) and Diffusion Tensor Imaging (DTI) are newly emerging techniques in Magnetic Resonance Imaging (MRI). These techniques enable studying connectivity and fibre orientations in different regions of the brain and also detecting abnormalities due to pathological conditions and physiological defects in the brain, which were not possible with conventional MRI techniques. One challenging area of research in DWI is the estimation of multiple diffusion compartments within individual voxels of a DWI image. The concept behind this estimation is that different regions of the brain have different diffusivities, and a single voxel in the image can contain more than one such diffusion component. This report presents our thorough study of multi-compartment estimation problem in DWI, focusing primarily on two compartment estimation problem due to two major types of diffusion compartments – water diffusion and vascular blood flow. There are two methods of estimation proposed in this study, both achieving accurate results when compared with the ground truth values. The algorithms are tested both on synthetic data as well as on actual brain data. MASTER OF ENGINEERING (SCE)