On Variant Strategies To Solve The Magnitude Least Squares Optimization Problem In Parallel Transmission Pulse Design And Under Strict SAR And Power Constraints

TL;DR

This paper explores various optimization strategies for designing parallel transmission RF pulses in MRI, focusing on magnitude least squares problems with strict SAR and hardware constraints, demonstrating efficient solutions suitable for routine use.

Contribution

It introduces and compares multiple optimization methods for MLS pulse design under strict constraints, providing practical recommendations and demonstrating fast, robust solutions.

Findings

Sequential quadratic programming (SQP) and interior point methods are effective.

The proposed methods achieve rapid pulse design within constraints.

Solutions are suitable for routine clinical MRI applications.

Abstract

Parallel transmission has been a very promising candidate technology to mitigate the inevitable radio-frequency field inhomogeneity in magnetic resonance imaging (MRI) at ultra-high field (UHF). For the first few years, pulse design utilizing this technique was expressed as a least squares problem with crude power regularizations aimed at controlling the specific absorption rate (SAR), hence the patient safety. This approach being suboptimal for many applications sensitive mostly to the magnitude of the spin excitation, and not its phase, the magnitude least squares (MLS) problem then was first formulated in 2007. Despite its importance and the availability of other powerful numerical optimization methods, this problem yet has been faced exclusively by the pulse designer with the so-called variable exchange method. In this paper, we investigate other strategies and incorporate directly the strict SAR and hardware constraints. Different schemes such as sequential quadratic programming (SQP), interior point (I-P) methods, semi-definite programming (SDP) and magnitude squared least squares (MSLS) relaxations are studied both in the small and large tip angle regimes with real data sets obtained in-vivo on a human brain at 7 Tesla. Convergence and robustness of the different approaches are analyzed, and recommendations to tackle this specific problem are finally given. Small tip angle and inversion pulses are returned in a few seconds and in under a minute respectively while respecting the constraints, allowing the use of the proposed approach in routine.