基于球面Haar紧框架的球面信号处理卷积神经网络
Convolutional Neural Networks for Spherical Signal Processing via Spherical Haar Tight Framelets
摘要：
在本文中，我们开发了一个一般的理论框架，用于构造Haar型紧框架上的任何紧集的层次划分。特别地，我们在2-球面上构造了一个新的面积正则层次划分，并建立了相应的具有方向性的球面Haar紧框架。最后，我们通过评估和说明我们的面积规则的球形Haar紧小框架在几个去噪实验的有效性。此外，我们提出了一个卷积神经网络（CNN）模型的球形信号去噪，采用快速小框架分解和重建算法。实验结果表明，我们提出的CNN模型优于阈值方法，并具有较强的泛化能力和鲁棒性。
英文摘要：
In this paper, we develop a general theoretical framework for constructing Haar-type tight framelets on any compact set with a hierarchical partition. In particular, we construct a novel area-regular hierarchical partition on the 2-sphere and establish its corresponding spherical Haar tight framelets with directionality. We conclude by evaluating and illustrating the effectiveness of our area-regular spherical Haar tight framelets in several denoising experiments. Furthermore, we propose a convolutional neural network (CNN) model for spherical signal denoising which employs the fast framelet decomposition and reconstruction algorithms. Experiment results show that our proposed CNN model outperforms threshold methods, and processes strong generalization and robustness properties.
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