Convolutional Neural Networks for Spherical Signal Processing via Area-Regular Spherical Haar Tight Framelets

Jianfei Li; Han Feng; Xiaosheng Zhuang

doi:10.1109/TNNLS.2022.3160169

Convolutional Neural Networks for Spherical Signal Processing via Area-Regular Spherical Haar Tight Framelets

Jianfei Li, Han Feng^*, Xiaosheng Zhuang

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

15 Citations (Scopus)

Abstract

In this article, 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 two spheres and establish its corresponding spherical Haar tight framelets with directionality. We conclude by evaluating and illustrate 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 fast framelet decomposition and reconstruction algorithms. Experiment results show that our proposed CNN model outperforms threshold methods and processes strong generalization and robustness. © 2022 IEEE.

Original language	English
Pages (from-to)	4400-4410
Journal	IEEE Transactions on Neural Networks and Learning Systems
Volume	35
Issue number	4
Online published	29 Mar 2022
DOIs	https://doi.org/10.1109/TNNLS.2022.3160169
Publication status	Published - Apr 2024

Funding

This work was supported in part by the Research Grants Council of the Hong Kong Special Administrative Region, China, under Project CityU 11306220, Project CityU 11302218, and Project C1013-21GF; and in part by the City University of Hong Kong under Project 7005497 and Project 7005603.

Research Keywords

Area regular
bounded domains
Convolution
convolutional neural network (CNN)
Convolutional neural networks
directional framelets
image denoising
Noise reduction
Robustness
Signal denoising
Signal representation
spherical Haar framelets
spherical signals
tight framelets
Urban areas

RGC Funding Information

RGC-funded

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10.1109/TNNLS.2022.3160169

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Cite this

@article{bbbca19c5de244d89a863f8d29dc0fd4,

title = "Convolutional Neural Networks for Spherical Signal Processing via Area-Regular Spherical Haar Tight Framelets",

abstract = "In this article, 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 two spheres and establish its corresponding spherical Haar tight framelets with directionality. We conclude by evaluating and illustrate 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 fast framelet decomposition and reconstruction algorithms. Experiment results show that our proposed CNN model outperforms threshold methods and processes strong generalization and robustness. {\textcopyright} 2022 IEEE.",

keywords = "Area regular, bounded domains, Convolution, convolutional neural network (CNN), Convolutional neural networks, directional framelets, image denoising, Noise reduction, Robustness, Signal denoising, Signal representation, spherical Haar framelets, spherical signals, tight framelets, Urban areas",

author = "Jianfei Li and Han Feng and Xiaosheng Zhuang",

year = "2024",

month = apr,

doi = "10.1109/TNNLS.2022.3160169",

language = "English",

volume = "35",

pages = "4400--4410",

journal = "IEEE Transactions on Neural Networks and Learning Systems",

issn = "2162-237X",

publisher = "IEEE Computational Intelligence Society",

number = "4",

}

TY - JOUR

T1 - Convolutional Neural Networks for Spherical Signal Processing via Area-Regular Spherical Haar Tight Framelets

AU - Li, Jianfei

AU - Feng, Han

AU - Zhuang, Xiaosheng

PY - 2024/4

Y1 - 2024/4

N2 - In this article, 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 two spheres and establish its corresponding spherical Haar tight framelets with directionality. We conclude by evaluating and illustrate 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 fast framelet decomposition and reconstruction algorithms. Experiment results show that our proposed CNN model outperforms threshold methods and processes strong generalization and robustness. © 2022 IEEE.

AB - In this article, 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 two spheres and establish its corresponding spherical Haar tight framelets with directionality. We conclude by evaluating and illustrate 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 fast framelet decomposition and reconstruction algorithms. Experiment results show that our proposed CNN model outperforms threshold methods and processes strong generalization and robustness. © 2022 IEEE.

KW - Area regular

KW - bounded domains

KW - Convolution

KW - convolutional neural network (CNN)

KW - Convolutional neural networks

KW - directional framelets

KW - image denoising

KW - Noise reduction

KW - Robustness

KW - Signal denoising

KW - Signal representation

KW - spherical Haar framelets

KW - spherical signals

KW - tight framelets

KW - Urban areas

UR - http://www.scopus.com/inward/record.url?scp=85127476048&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85127476048&origin=recordpage

U2 - 10.1109/TNNLS.2022.3160169

DO - 10.1109/TNNLS.2022.3160169

M3 - RGC 21 - Publication in refereed journal

SN - 2162-237X

VL - 35

SP - 4400

EP - 4410

JO - IEEE Transactions on Neural Networks and Learning Systems

JF - IEEE Transactions on Neural Networks and Learning Systems

IS - 4

ER -

Convolutional Neural Networks for Spherical Signal Processing via Area-Regular Spherical Haar Tight Framelets

Abstract

Funding

Research Keywords

RGC Funding Information

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GRF: Approximation Theory of Integral Discretization on High Dimensional Domains

GRF: Multiscale Data Analysis: Directional Framelets on Manifolds and Graphs

Cite this

Convolutional Neural Networks for Spherical Signal Processing via Area-Regular Spherical Haar Tight Framelets

Abstract

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Projects

GRF: Approximation Theory of Integral Discretization on High Dimensional Domains

GRF: Multiscale Data Analysis: Directional Framelets on Manifolds and Graphs

Cite this