PDE-BASED DENOISING TECHNIQUE IN MREIT
Byung Il Leea, Suk Ho Leeb, Tae-Seong Kima, Jin Keun Seob, Ohin Kwonc, and Eung Je Wooa
a
Kyung Hee University, Kyungki 449-701, Korea
b
Yonsei University, Seoul 120-749, Korea
c
Konkuk University, Seoul 143-701, Korea
In Magnetic Resonance Electrical Impedance Tomography (MREIT), we try to visualize cross-sectional
images of conductivity distributions inside an electrically conducting subject. Several conductivity image
reconstruction algorithms have been developed based on the measurement of only one component such as
Bz of the magnetic flux density B = (Bx, By, Bz) [1-2]. However, the measured data Bz in MREIT is usually
degraded in its accuracy due to the non-ideal data acquisition system of an MR scanner. Furthermore,
numerical computations of Bz or 2Bz in the developed conductivity reconstruction algorithms such as
the harmonic Bz algorithm [1] and the gradient Bz decomposition algorithm [2] tend to amplify the noise in
Bz. Hence, it is necessary to develop an efficient denoising technique that eliminates the random noise in
the Bz signal while preserving important features.
We have to change the problem into a form which is easier to handle. We use a kind of decomposition
technique which decomposes the original noisy Bz data into a smooth part and a noisy high-frequency part
as
Bz = Bzs + Bzn. (1)
After denoising each decomposed part independently using different denoising techniques, the noise-
removed parts are combined together to result in a noise-removed Bz data. Therefore, we propose a PDE-
based denoising technique which shuts the diffusion process off at the peaks. However, we have to judge
whether a peak indicates an edge or noise. In order to do this, we need to trace the location of the edges.
This can be done by using the information given by the corresponding MR magnitude image M. This can
be achieved by solving the following diffusion equation in the corresponding imaging slice with its
boundary .
u 1
g u 0
in
t M
(2)
u ( x, y ,0) Bz ( x, y ) on
n
where g is an increasing function with g(0) = 0 and lims g (s) .
Numerical results show that the reconstruction algorithm with the denoised Bz data successfully
reconstruct the conductivity image. The proposed denoising technique is based on a kind of harmonic
interpolator using its neighbouring noisy Bz data and concentrated on the noisy high-frequency part Bzn. In
a homogeneous medium, Bzn would be constant plus an added noisy.
Acknowledgements: This work was supported by the grant R11-2002-103 from Korea Science and
Engineering Foundation.
REFERENCES
1. S. H. Oh, B. I. Lee, E. J. Woo, S. Y. Lee, M. H. Cho, O. Kwon, and J. K. Seo, “Conductivity and current density
image reconstruction using harmonic Bz algorithm in magnetic resonance electrical impedance tomography,”
Phys. Med. Biol., vol. 48, pp. 3101-16, 2003.
2. C. Park, O. Kwon, E. J. Woo, and J. K. Seo, “Electrical conductivity imaging using gradient Bz decomposition
algorithm in magnetic resonance electrical impedance tomography (MREIT),” IEEE Trans. Med. Imag., vol. 23,
pp. 388-94, 2004.