Multiscale transforms have become a key ingredient in many data processing tasks. With technological development, we observe a growing demand for methods to cope with non-linear data structures such as manifold values. In this paper, we propose a multiscale approach for analyzing manifold-valued data using a pyramid transform. The transform uses a unique class of downsampling operators that enable a non-interpolating subdivision schemes as upsampling operators. We describe this construction in detail and present its analytical properties, including stability and coefficient decay. Next, we numerically demonstrate the results and show the application of our method to denoising and anomaly detection.

翻译：多尺度变换已成为许多数据处理任务的一个关键要素。 随着技术发展,我们观察到对处理多种值等非线性数据结构的方法的需求日益增加。 在本文中,我们提出使用金字塔变换分析多重价值数据的多尺度方法。变换使用独特的下层抽样操作员类别,使非内插的分层计划成为升级操作员。我们详细描述这一构造,并展示其分析特性,包括稳定性和系数衰减。接下来,我们用数字来展示结果,并展示我们用来分辨和发现异常现象的方法的应用。