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Diffusion tensor imaging (DTI) has been widely used for nondestructive characterization of microstructures of myocardium or brain connectivity. It requires repeated acquisition with different diffusion gradients. The long acquisition time greatly limits the clinical application of DTI. In this paper, a novel method, named model-based method with joint sparsity constraint (MB-JSC), effectively incorporates the prior information on the joint sparsity of different diffusion-weighted images in direct estimation of the diffusion tensor from highly undersampled k-space data. Experimental results demonstrate that the proposed method is able to estimate the diffusion tensors more accurately than the existing method when a high net reduction factor is used.