Numerical Solution Of An Inverse Problem In
Magnetic Resonance Imaging Using A Regularized
Higher-order Boundary Element Method
Author(s)
L. Marin, H. Power, R. W. Bowtell, C. Cobos Sanchez,
A. A. Becker, P. Glover & I. A. Jones
Abstract
We investigate the reconstruction of a divergence-free surface current distribution
from knowledge of the magnetic flux density in a prescribed region of interest
in the framework of static electromagnetism. This inverse problem is motivated
by the design of gradient coils used in magnetic resonance imaging (MRI) and
is formulated using its corresponding integral representation according to potential
theory. A novel higher-order boundary element method (BEM) which satis-
fies the continuity equation for the current density, i.e. divergence-free BEM, is
also presented. Since the discretised BEM system is ill-posed and hence the associated
least-squares solution may be inaccurate and/or physically meaningless,
the Tikhonov regularization method is employed in order to retrieve accurate and
physically correct solutions.
Keywords: inverse problem, regularization, divergence-free BEM, magnetic resonance
imaging (MRI).
1 Introduction
Magnetic resonance imaging (MRI) is a non-invasive technique for imaging the
human body, which has revolutionised the field of diagnostic medicine.MRI relies
on the generation of highly controlled magnetic fields that are essential to the process
of image production. In particular, an extremely homogeneous, strong, static
Keywords
inverse problem, regularization, divergence-free BEM, magnetic resonance
imaging (MRI).
Related Book
Other papers in this volume
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