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

arXiv: https://arxiv.org/abs/2201.07890 · HTML: https://mlsanity.com/paper/2201.07890/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 43 references that are in the map.
- First posted on arXiv 17 Jan 2022.

## Builds on (most cited first, 6 of 6)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [Understanding Deep Convolutional Networks](https://mlsanity.com/paper/1601.04920/) (2016)
- [Deep Learning in the Wavelet Domain](https://mlsanity.com/paper/1811.06115/) (2018)
- [Adaptive directional Haar tight framelets on bounded domains for digraph signal representations](https://mlsanity.com/paper/2008.11966/) (2020)

## Built on by (most cited first, 5 of 5)

- [Permutation Equivariant Graph Framelets for Heterophilous Graph Learning](https://mlsanity.com/paper/2306.04265/) (2023)
- [SignReLU neural network and its approximation ability](https://mlsanity.com/paper/2210.10264/) (2022)
- [Spherical Image Inpainting with Frame Transformation and Data-driven Prior Deep Networks](https://mlsanity.com/paper/2209.14604/) (2022)
- [CHEM: Estimating and Understanding Hallucinations in Deep Learning for Image Processing](https://mlsanity.com/paper/2512.09806/) (2025)
- [Data-Adaptive Graph Framelets with Generalized Vanishing Moments for Graph Machine Learning](https://mlsanity.com/paper/2309.03537/) (2023)

## Abstract (arXiv)

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.