Convolutional Neural Networks for Spherical Signal Processing via Spherical Haar Tight Framelets
This addresses spherical signal processing for applications like geophysics or astronomy, representing an incremental improvement through a novel hybrid approach.
The authors tackled spherical signal denoising by constructing area-regular spherical Haar tight framelets and integrating them into a CNN model, achieving superior performance over threshold methods with demonstrated generalization and robustness.
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.