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NMR Biomed. 2014 Mar;27(3):312-9. doi: 10.1002/nbm.3064. Epub 2014 Jan 7.

Background field removal by solving the Laplacian boundary value problem.

Author information

1
Department of Radiology, Weill Cornell Medical College, New York, NY, USA.

Abstract

The removal of the background magnetic field is a critical step in generating phase images and quantitative susceptibility maps, which have recently been receiving increasing attention. Although it is known that the background field satisfies Laplace's equation, the boundary values of the background field for the region of interest have not been explicitly addressed in the existing methods, and they are not directly available from MRI measurements. In this paper, we assume simple boundary conditions and remove the background field by explicitly solving the boundary value problems of Laplace's or Poisson's equation. The proposed Laplacian boundary value (LBV) method for background field removal retains data near the boundary and is computationally efficient. Tests on a numerical phantom and an experimental phantom showed that LBV was more accurate than two existing methods.

KEYWORDS:

Laplace's equation; Poisson's equation; background field removal; boundary value problem of partial differential equation (PDE); full multigrid (FMG) algorithm; phase imaging; quantitative susceptibility mapping (QSM); susceptibility weighted imaging (SWI)

PMID:
24395595
DOI:
10.1002/nbm.3064
[Indexed for MEDLINE]

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