Algorithms for Least-Squares Noncartesian MR Image Reconstruction

TL;DR

This paper compares iterative least-squares methods for noncartesian MRI reconstruction, highlighting the advantages of the LSMR algorithm over the traditional Conjugate Gradient approach in terms of numerical stability.

Contribution

It introduces the LSMR algorithm as a superior alternative for noncartesian MRI reconstruction when Toeplitz embedding is not applicable.

Findings

LSMR has better numerical stability than Conjugate Gradient.

LSMR is preferable when Toeplitz embedding cannot be used.

The paper provides practical guidance for MRI reconstruction algorithms.

Abstract

Iterative least-squares MR reconstructions typically use the Conjugate Gradient algorithm, despite known numerical issues. This paper demonstrates that the more recent LSMR algorithm has favourable numerical properties, and is to be preferred in situations where Toeplitz embedding cannot be used to accelerate the Conjugate Gradient method.