SIAM Journal on Imaging Sciences, Volume 13, Issue 3, Page 1386-1414, January 2020.
Vector fields arise in a variety of quantity measure and visualization techniques, such as fluid flow imaging, motion estimation, deformation measures, and color imaging, leading to a better understanding of physical phenomena. Recent progress in vector field imaging technologies has emphasized the need for efficient noise removal and reconstruction algorithms. A key ingredient in the successful extraction of signals from noisy measurements is prior information, which can often be represented as a parameterized model. In this work, we extend the overparameterization variational framework in order to perform model-based reconstruction of vector fields. The overparameterization methodology combines local modeling of the data with global model parameter regularization. By considering the vector field as a linear combination of basis vector fields and appropriate scale and rotation coefficients, we can reduce the denoising problem to a simpler form of coefficient recovery. We introduce two versions of the overparameterization framework: a total variation-based method and a sparsity-based method, which relies on the cosparse analysis model. We demonstrate the efficiency of the proposed frameworks for two- and three-dimensional vector fields with linear and quadratic overparameterization models.

中文翻译：

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向量场的超参数化模型

SIAM影像科学杂志，第13卷，第3期，第1386-1414页，2020年1月。
向量场出现在各种数量的度量和可视化技术中，例如流体流动成像，运动估计，变形度量和彩色成像，从而可以更好地理解物理现象。矢量场成像技术的最新进展强调了对有效噪声去除和重构算法的需求。从噪声测量中成功提取信号的关键因素是先验信息，该信息通常可以表示为参数化模型。在这项工作中，我们扩展了超参数化变分框架，以执行基于模型的矢量场重构。超参数化方法将数据的局部建模与全局模型参数正则化结合在一起。通过将向量场视为基本向量场与适当的比例和旋转系数的线性组合，我们可以将去噪问题简化为系数恢复的简单形式。我们介绍了过度参数化框架的两个版本：基于总变化的方法和基于稀疏性的方法，它们依赖于稀疏分析模型。我们用线性和二次过参数化模型证明了针对二维和三维矢量场的拟议框架的效率。