  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.
