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

Abstract: 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) and patterns with a single choice of parameters (no parameter tuning). We show that our proposed algorithms, alternating Gradient Descent (GD) and minimization for MRI (altGDmin-MRI and altGDmin-MRI2), outperform many existing approaches while also being faster than all of them, on average. This claim is based on comparisons on 8 different retrospectively undersampled single- or multi-coil dynamic MRI applications, undersampled using either 1D Cartesian or 2D pseudo-radial undersampling at multiple sampling rates. All comparisons used the same set of algorithm parameters. Our second contribution is a mini-batch and a fully online extension that can process new measurements and return reconstructions either as soon as measurements of a new image frame arrive, or after a short delay.