Hokkaido University, Sapporo 060-0810, Japan.
Comput Math Methods Med. 2013;2013:912920. doi: 10.1155/2013/912920. Epub 2013 Apr 4.
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.
对于被称为 MRE（磁共振弹性成像）的诊断方式，可以测量在人体组织中传播的波的位移矢量。从该测量数据中得出的局部波长的平均值可以作为诊断的指标，因为当组织变硬时，局部波长会变大。通过假设波的局部形式近似为多个复平面波，我们通过首先应用具有适当大小的高斯窗口的 FBI 变换（傅里叶-布罗伊格-伊戈利纳泽变换），然后对傅里叶变量取变换的模的最大值，来识别多个复平面波中的最强平面波的复线性相位的实部。线性相位的实部只不过是波矢量和位置矢量的实内积。同样，线性相位的虚部描述了波的衰减，它被表示为实向量和位置向量的实内积。这个向量也可以通过我们的方法来恢复。我们还将这些方法应用于设计噪声 MRE 数据的一些去噪和滤波。
