Inverse Problems in Magnetic Resonance Velocimetry: Shape, Forcing and Boundary Condition Inference

A. Kontogiannis, M. Juniper
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引用次数: 1

Abstract

We derive and implement an algorithm that takes noisy magnetic resonance velocimetry (MRV) images of Stokes flow and infers the velocity field, the most likely position of the boundary, the inlet and outlet boundary conditions, and any body forces. We do this by minimizing a discrepancy norm of the velocity fields between the MRV experiment and the Stokes problem, and at the same time we obtain a filtered (denoised) version of the original MRV image. We describe two possible approaches to regularize the inverse problem, using either a variational technique, or Gaussian random fields. We test the algorithm for flows governed by a Poisson or a Stokes problem, using both real and synthetic MRV measurements. We find that the algorithm is capable of reconstructing the shape of the domain from artificial images with a low signal-to-noise ratio.
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磁共振测速中的逆问题:形状、强迫和边界条件推断
我们推导并实现了一种算法,该算法采用Stokes流的噪声磁共振测速(MRV)图像,并推断速度场,边界最可能的位置,入口和出口边界条件以及任何物体力。我们通过最小化MRV实验和Stokes问题之间的速度场差异范数来实现这一点,同时我们获得原始MRV图像的滤波(去噪)版本。我们描述了两种可能的方法来正则化逆问题,使用变分技术或高斯随机场。我们使用真实的和合成的MRV测量来测试由泊松或斯托克斯问题控制的流的算法。我们发现该算法能够以较低的信噪比从人工图像中重建区域形状。
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