In this paper, we propose mathematical models for reconstructing the optical flow in time-harmonic elastography. In this image acquisition technique, the object undergoes a special time-harmonic oscillation with known frequency so that only the spatially varying amplitude of the velocity field has to be determined. This allows for a simpler multi-frame optical flow analysis using Fourier analytic tools in time. We propose three variational optical flow models and show how their minimization can be tackled via Fourier transform in time. Numerical examples with synthetic as well as real-world data demonstrate the benefits of our approach. Keywords: optical flow, elastography, Fourier transform, iteratively reweighted least squares, Horn--Schunck method

翻译：本文提出了用于重建时谐弹性成像中光流的数学模型。在该图像采集技术中，物体以已知频率进行特殊时谐振荡，因此仅需确定速度场的空间变化振幅。这使得我们能够利用时间傅里叶分析工具进行更简化的多帧光流分析。我们提出了三种变分光流模型，并展示了如何通过时间傅里叶变换实现其最小化求解。合成数据与真实数据的数值实验验证了所提方法的优势。关键词：光流，弹性成像，傅里叶变换，迭代重加权最小二乘法，Horn--Schunck方法