Compression of volume-surface integral equation matrices via Tucker decomposition for magnetic resonance applications

TL;DR

This paper introduces a Tucker decomposition-based compression method for volume-surface integral equation matrices in MRI, enabling fast GPU-accelerated electromagnetic simulations at high resolution by drastically reducing memory requirements.

Contribution

The authors develop a novel tensor-based compression technique for VSIE matrices that, combined with adaptive cross approximation, allows efficient MRI simulations at clinical resolutions.

Findings

Matrix compression reduces memory from 80 TB to 43 MB.

GPU-based matrix-vector products are performed in approximately 33 seconds.

The method enables feasible high-resolution MRI electromagnetic simulations.

Abstract

In this work, we propose a method for the compression of the coupling matrix in volume\hyp surface integral equation (VSIE) formulations. VSIE methods are used for electromagnetic analysis in magnetic resonance imaging (MRI) applications, for which the coupling matrix models the interactions between the coil and the body. We showed that these effects can be represented as independent interactions between remote elements in 3D tensor formats, and subsequently decomposed with the Tucker model. Our method can work in tandem with the adaptive cross approximation technique to provide fast solutions of VSIE problems. We demonstrated that our compression approaches can enable the use of VSIE matrices of prohibitive memory requirements, by allowing the effective use of modern graphical processing units (GPUs) to accelerate the arising matrix\hyp vector products. This is critical to enable numerical MRI simulations at clinical voxel resolutions in a feasible computation time. In this paper, we demonstrate that the VSIE matrix\hyp vector products needed to calculate the electromagnetic field produced by an MRI coil inside a numerical body model with $1$ mm$^3$ voxel resolution, could be performed in $\sim 33$ seconds in a GPU, after compressing the associated coupling matrix from $\sim 80$ TB to $\sim 43$ MB.