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In this paper, we develop a general theoretical framework for constructingHaar-type tight framelets on any compact set with a hierarchical partition. Inparticular, we construct a novel area-regular hierarchical partition on the2-sphere and establish its corresponding spherical Haar tight framelets withdirectionality. We conclude by evaluating and illustrating the effectiveness ofour area-regular spherical Haar tight framelets in several denoisingexperiments. Furthermore, we propose a convolutional neural network (CNN) modelfor spherical signal denoising which employs the fast framelet decompositionand reconstruction algorithms. Experiment results show that our proposed CNNmodel outperforms threshold methods, and processes strong generalization androbustness properties.

Convolutional Neural Networks for Spherical Signal Processing via Spherical Haar Tight Framelets