並列タイトル等Magnetic Resonance Elastography に対する数値解析の新方法
一般注記For the diagnosing modality called MRE (Magnetic Resonance Elastogra-phy), the displacement vector of a wave propagating in a human tissue can bemeasured. The average of the local wave length of the wave from this mea-sured data could be an index for the diagnosing, because the local wave lengthbecomes larger when the tissue is stiffer. By assuming that the local form ofthe wave is given approximately as multiple complex plane waves, we identifythe real part of the complex linear phase of the strongest plane wave of thismultiple complex plane waves, by first applying the FBI transform (Fourier-Bros-Iagolnitzer transform) with an appropriate size of Gaussian window andthen taking the maximum of the modulus of the transform with respect to theFourier variable. We call this method LWV method. The real part of the linearphase is nothing but the real inner product of the wave vector and the positionvector. Similarly the imaginary part of the linear phase describes the attenu-ation of the wave and it is given as a real inner product of a real vector andthe position vector. This vector can also be recovered by our method calledthe LAV method. We also apply these methods to design some de-noising andfiltering for noisy MRE data. Although we restricted applying our methods toMRE wave images, it can also be applied to other wave images.
(主査) 教授 利根川 吉廣, 教授 神保 秀一, 教授 中村 玄 (Inha University, KOREA), 准教授 荒井 迅
理学院(数学専攻)
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受理日(W3CDTF)2015-02-03T05:25:05+09:00
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