  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.
