Accelerated dynamic MRI using structured low rank matrix completion

We introduce a fast structured low-rank matrix completion algorithm with low memory & computational demand to recover the dynamic MRI data from undersampled measurements. The 3-D dataset is modeled as a piecewise smooth signal, whose discontinuities are localized to the zero sets of a bandlimited function. We show that a structured matrix corresponding to convolution with the Fourier coefficients of the signal derivatives is highly low-rank. This property enables us to recover the signal from undersampled measurements. The application of this scheme in dynamic MRI shows significant improvement over state of the art methods.