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Computational and Mathematical Methods in Medicine
Volume 2013 (2013), Article ID 912920, 11 pages
http://dx.doi.org/10.1155/2013/912920
Research Article

Model Independent MRE Data Analysis

1Hokkaido University, Sapporo 060-0810, Japan
2Inha University, Incheon 402-751, Republic of Korea

Received 27 November 2012; Accepted 16 January 2013

Academic Editor: Jin Keun Seo

Copyright © 2013 Kogo Yoshikawa and Gen Nakamura. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For the diagnosing modality called MRE (magnetic resonance elastography), the displacement vector of a wave propagating in a human tissue can be measured. The average of the local wavelength from this measured data could be an index for the diagnosing, because the local wave length becomes larger when the tissue is stiffer. By assuming that the local form of the wave is given approximately as multiple complex plane waves, we identify the real part of the complex linear phase of the strongest plane wave of this multiple complex plane waves, by first applying the FBI transform (Fourier-Bros-Iagolnitzer transform) with an appropriate size of Gaussian window and then taking the maximum of the modulus of the transform with respect to the Fourier variable. The real part of the linear phase is nothing but the real inner product of the wave vector and the position vector. Similarly the imaginary part of the linear phase describes the attenuation of the wave and it is given as a real inner product of a real vector and the position vector. This vector can also be recovered by our method. We also apply these methods to design some denoising and filtering for noisy MRE data.