论文标题
B-Spline模型的自适应正则化科学数据
Adaptive Regularization of B-Spline Models for Scientific Data
论文作者
论文摘要
B-Spline模型是代表具有功能近似的科学数据集的强大方法。但是，当要近似的数据不均匀分布时，这些模型可能会遭受虚假振荡。传统上，模型正则化（即平滑）被用来最大程度地减少这些振荡。不幸的是，如果不平滑数据集的关键特征，有时不可能充分删除不需要的工件。在本文中，我们提出了一种模型正则化方法，该方法可保留数据集的重要特征，同时最大程度地减少人工振荡。我们的方法会自动在整个域中的平滑参数的强度变化，从而消除了受限制区域的伪像，同时使其他区域保持不变。我们方法的行为在科学模拟产生的二维数据集的集合中得到了验证。
B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model regularization (i.e., smoothing) has traditionally been used to minimize these oscillations; unfortunately, it is sometimes impossible to sufficiently remove unwanted artifacts without smoothing away key features of the data set. In this article, we present a method of model regularization that preserves significant features of a data set while minimizing artificial oscillations. Our method varies the strength of a smoothing parameter throughout the domain automatically, removing artifacts in poorly-constrained regions while leaving other regions unchanged. The behavior of our method is validated on a collection of two- and three-dimensional data sets produced by scientific simulations.
