论文标题
天文图的多尺度分解 - 一种约束的扩散法
Multi-scale decomposition of astronomical maps -- a constrained diffusion method
论文作者
论文摘要
我们提出了一种新的，有效的多尺度方法，将映射（或一般信号）分解为包含不同尺寸结构的组件图。在广泛使用的波变换中，由于施加带限制的过滤器，围绕具有急剧过渡的区域出现了包含负值的伪影。在我们的方法中，分解是通过求解扩散方程的修改的非线性版本来实现的。这是受各向异性扩散方法的启发，该方法在图像过滤和部分微分方程之间建立了联系。在我们的情况下，在保证分解图像的积极性的地方解决了工件问题。我们的新方法特别适用于包含局部非线性特征的信号，这是天文观测的典型特征。它可用于定量研究天文图的多尺度结构，并应在与观察相关的任务（例如背景删除）中有用。因此，我们提出了一种称为“比例尺频谱”的新方法，该方法描述了图像值如何在比例空间中的不同组件之间分布，以描述地图。该方法允许输入数量的尺寸数组，并在附录中包含python3实现算法，并在https://gxli.github.io/concontain-diffusion-diffusion-decomposition/上找到。
We propose a new, efficient multi-scale method to decompose a map (or signal in general) into components maps that contain structures of different sizes. In the widely-used wave transform, artifacts containing negative values arise around regions with sharp transitions due to the application of band-limited filters. In our approach, the decomposition is achieved by solving a modified, non-linear version of the diffusion equation. This is inspired by the anisotropic diffusion methods, which establish the link between image filtering and partial differential equations. In our case, the artifact issue is addressed where the positivity of the decomposed images is guaranteed. Our new method is particularly suitable for signals which contain localized, non-linear features, as typical of astronomical observations. It can be used to study the multi-scale structures of astronomical maps quantitatively and should be useful in observation-related tasks such as background removal. We thus propose a new measure called the "scale spectrum", which describes how the image values distribute among different components in the scale space, to describe maps. The method allows for input arrays of an arbitrary number of dimensions, and a python3 implementation of the algorithms is included in the Appendix and available at https://gxli.github.io/Constrained-Diffusion-Decomposition/.
