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

TL;DR

This paper introduces fast, memory-efficient gradient descent algorithms for accelerated dynamic MRI reconstruction using a low-rank matrix model, outperforming existing methods across various sampling schemes and rates.

Contribution

The novel GD-based algorithms (altGDmin-MRI1 and altGDmin-MRI2) are faster, more memory-efficient, and more general than existing approaches, with a hierarchical low-rank model for dynamic MRI.

Findings

Outperforms popular existing methods in speed and accuracy

Effective across multiple sampling schemes and rates

Demonstrated on 8 retrospective and some prospective datasets

Abstract

This work develops a novel set of algorithms, alternating Gradient Descent (GD) and minimization for MRI (altGDmin-MRI1 and altGDmin-MRI2), for accelerated dynamic MRI by assuming an approximate low-rank (LR) model on the matrix formed by the vectorized images of the sequence. The LR model itself is well-known in the MRI literature; our contribution is the novel GD-based algorithms which are much faster, memory efficient, and general compared with existing work; and careful use of a 3-level hierarchical LR model. By general, we mean that, with a single choice of parameters, our method provides accurate reconstructions for multiple accelerated dynamic MRI applications, multiple sampling rates and sampling schemes. We show that our methods outperform many of the popular existing approaches while also being faster than all of them, on average. This claim is based on comparisons on 8 different retrospectively under sampled multi-coil dynamic MRI applications, sampled using either 1D Cartesian or 2D pseudo radial under sampling, at multiple sampling rates. Evaluations on some prospectively under sampled datasets are also provided. Our second contribution is a mini-batch subspace tracking extension that can process new measurements and return reconstructions within a short delay after they arrive. The recovery algorithm itself is also faster than its batch counterpart.