  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.
