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

TL;DR

This paper introduces a new theoretical framework for spherical Haar tight framelets, constructs a novel hierarchical partition on the 2-sphere, and develops a CNN model that outperforms existing denoising methods with strong robustness.

Contribution

It presents a novel hierarchical partition on the 2-sphere, constructs spherical Haar tight framelets, and proposes a CNN model leveraging these framelets for improved spherical signal denoising.

Findings

The spherical Haar tight framelets effectively denoise signals.

The CNN model outperforms traditional threshold methods.

The approach demonstrates strong generalization and robustness.

Abstract

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.