论文标题
用度量双积分的扩散张量正规化
Diffusion Tensor Regularization with Metric Double Integrals
论文作者
论文摘要
在本文中，我们提出了一种差异正则化方法，用于降级和介入扩散张量磁共振图像。我们将这些图像视为流动性sobolev函数，即在无限的尺寸设置中，适当地定义。正则函数定义为双积分，相当于欧几里得设置中的sobolev半数。我们扩展了对Ciak，Melching和Scherzer的分析，“与一组矢量中值的度量双重积分和值的定期化”，载于：关于稳定性的数学成像与视觉和视觉杂志（2019年），与唯一性结果的变量正则化方法的收敛性，将它们应用于扩散探测器处理的构造和实际模型的模型和数字模型中，并将其应用于合成和数字中。
In this paper we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting, which are defined appropriately. The regularization functionals are defined as double integrals, which are equivalent to Sobolev semi-norms in the Euclidean setting. We extend the analysis of Ciak, Melching and Scherzer "Regularization with Metric Double Integrals of Functions with Values in a Set of Vectors", in: Journal of Mathematical Imaging and Vision (2019) concerning stability and convergence of the variational regularization methods by a uniqueness result, apply them to diffusion tensor processing, and validate our model in numerical examples with synthetic and real data.
