Fast Low Rank column-wise Compressive Sensing for Accelerated Dynamic MRI

This work develops a fast, memory-efficient, and general algorithm for accelerated/undersampled dynamic MRI by assuming an approximate LR model on the matrix formed by the vectorized images of the sequence. By general, we mean that our algorithm can be used for multiple accelerated dynamic MRI applications and multiple sampling rates (acceleration rates) without any parameter changes. We show that our proposed algorithm, alternating Gradient Descent (GD) and minimization for MRI (altGDmin-MRI), outperforms many existing approaches on 6 different dynamic MRI applications, while also being faster (or much faster) than all of them. Our second contribution is a fully online and mini-batch extensions of this algorithm that can process new measurements and return reconstructions either as soon as measurements of a new image frame arrive, or after a short mini-batch of measurement vectors arrives.