We propose a two-stage algorithm for the super-resolution of MR images from their low-frequency k-space samples. In the first stage we estimate a resolution-independent mask whose zeros represent the edges of the image. This builds off recent work extending the theory of sampling signals of finite rate of innovation (FRI) to two-dimensional curves. We enable its application to MRI by proposing extensions of the signal models allowed by FRI theory, and by developing a more robust and efficient means to determine the edge mask. In the second stage of the scheme, we recover the super-resolved MR image using the discretized edge mask as an image prior. We evaluate our scheme on simulated single-coil MR data obtained from analytical phantoms, and compare against total variation reconstructions. Our experiments show improved performance in both noiseless and noisy settings.
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