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Diffusion-weighted imaging (DWI) provides invaluable information in white matter microstructure and is widely applied in neurological applications. However, DWI is largely limited by its relatively low spatial resolution. In this paper, we propose an image post-processing method, referred to as super-resolution reconstruction, to estimate a high spatial resolution DWI from the input low-resolution DWI, e.g., at a factor of 2. Instead of requiring specially designed DWI acquisition of multiple shifted or orthogonal scans, our method needs only a single DWI scan. To do that, we propose to model both the blurring and downsampling effects in the image degradation process where the low-resolution image is observed from the latent high-resolution image, and recover the latent high-resolution image with the help of two regularizations. The first regularization is four-dimensional (4D) low-rank, proposed to gather self …