Wavelets on Intervals for Image Denoising

Quanhan Li; Michelle Michelle; Bin Han; Xiaosheng Zhuang

doi:10.1109/SampTA64769.2025.11133491

Wavelets on Intervals for Image Denoising

Quanhan Li
, Michelle Michelle
, Bin Han
, Xiaosheng Zhuang

Department of Mathematics

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

Abstract

The method of obtaining (bi)-orthogonal wavelets on intervals (boundary wavelets) by a direct approach is employed. The tensor product can then be applied for the construction of high-dimensional boundary wavelets. The ℓ₁ optimization model integrating with such high-dimensional boundary wavelets for regularization was then used for image denoising and can be solved through the ADMM algorithm. Comparisons with the traditional wavelets (without boundary) are done to demonstrate the effectiveness of boundary wavelets and the advantages of the model with ADMM in the presence of large noise levels. ©2025 IEEE.

Original language	English
Title of host publication	2025 International Conference on Sampling Theory and Applications (SampTA)
Publisher	IEEE
Number of pages	4
ISBN (Electronic)	979-8-3315-0250-8
ISBN (Print)	979-8-3315-0251-5
DOIs	https://doi.org/10.1109/SampTA64769.2025.11133491
Publication status	Published - 2025
Event	15th International Conference on Sampling Theory and Applications (SampTA 2025) - University of Vienna, Vienna, Austria Duration: 28 Jul 2025 → 1 Aug 2025

Publication series

Name	International Conference on Sampling Theory and Applications
ISSN (Print)	2831-5480
ISSN (Electronic)	2694-0108

Conference

Conference	15th International Conference on Sampling Theory and Applications (SampTA 2025)
Place	Austria
City	Vienna
Period	28/07/25 → 1/08/25

Funding

B. Han was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grant RGPIN 2024-04991. X. Zhuang was supported in part by the Research Grants Council of Hong Kong (Project nos.: CityU 11309122, CityU 11302023, CityU 11301224), a grant from the Innovation and Technology Commission of Hong Kong (Project no. MHP/054/22), and a grant from the National Natural Science Foundation of China (NSFC 12471400).

Research Keywords

Wavelets on intervals
ℓ1 optimization model
ADMM
image denoising

RGC Funding Information

RGC-funded

Access Output

10.1109/SampTA64769.2025.11133491

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@inproceedings{16bc6cb00abf4590abda97367161f714,

title = "Wavelets on Intervals for Image Denoising",

abstract = "The method of obtaining (bi)-orthogonal wavelets on intervals (boundary wavelets) by a direct approach is employed. The tensor product can then be applied for the construction of high-dimensional boundary wavelets. The ℓ1 optimization model integrating with such high-dimensional boundary wavelets for regularization was then used for image denoising and can be solved through the ADMM algorithm. Comparisons with the traditional wavelets (without boundary) are done to demonstrate the effectiveness of boundary wavelets and the advantages of the model with ADMM in the presence of large noise levels. {\textcopyright}2025 IEEE.",

keywords = "Wavelets on intervals, ℓ1 optimization model, ADMM, image denoising",

author = "Quanhan Li and Michelle Michelle and Bin Han and Xiaosheng Zhuang",

year = "2025",

doi = "10.1109/SampTA64769.2025.11133491",

language = "English",

isbn = "979-8-3315-0251-5",

series = "International Conference on Sampling Theory and Applications",

publisher = "IEEE",

booktitle = "2025 International Conference on Sampling Theory and Applications (SampTA)",

address = "United States",

note = "15th International Conference on Sampling Theory and Applications (SampTA 2025) ; Conference date: 28-07-2025 Through 01-08-2025",

}

Li, Q, Michelle, M, Han, B & Zhuang, X 2025, Wavelets on Intervals for Image Denoising. in 2025 International Conference on Sampling Theory and Applications (SampTA). International Conference on Sampling Theory and Applications, IEEE, 15th International Conference on Sampling Theory and Applications (SampTA 2025), Vienna, Austria, 28/07/25. https://doi.org/10.1109/SampTA64769.2025.11133491

Wavelets on Intervals for Image Denoising. / Li, Quanhan; Michelle, Michelle; Han, Bin et al.
2025 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2025. (International Conference on Sampling Theory and Applications).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Wavelets on Intervals for Image Denoising

AU - Li, Quanhan

AU - Michelle, Michelle

AU - Han, Bin

AU - Zhuang, Xiaosheng

PY - 2025

Y1 - 2025

N2 - The method of obtaining (bi)-orthogonal wavelets on intervals (boundary wavelets) by a direct approach is employed. The tensor product can then be applied for the construction of high-dimensional boundary wavelets. The ℓ1 optimization model integrating with such high-dimensional boundary wavelets for regularization was then used for image denoising and can be solved through the ADMM algorithm. Comparisons with the traditional wavelets (without boundary) are done to demonstrate the effectiveness of boundary wavelets and the advantages of the model with ADMM in the presence of large noise levels. ©2025 IEEE.

AB - The method of obtaining (bi)-orthogonal wavelets on intervals (boundary wavelets) by a direct approach is employed. The tensor product can then be applied for the construction of high-dimensional boundary wavelets. The ℓ1 optimization model integrating with such high-dimensional boundary wavelets for regularization was then used for image denoising and can be solved through the ADMM algorithm. Comparisons with the traditional wavelets (without boundary) are done to demonstrate the effectiveness of boundary wavelets and the advantages of the model with ADMM in the presence of large noise levels. ©2025 IEEE.

KW - Wavelets on intervals

KW - ℓ1 optimization model

KW - ADMM

KW - image denoising

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001575485600002

U2 - 10.1109/SampTA64769.2025.11133491

DO - 10.1109/SampTA64769.2025.11133491

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 979-8-3315-0251-5

T3 - International Conference on Sampling Theory and Applications

BT - 2025 International Conference on Sampling Theory and Applications (SampTA)

PB - IEEE

T2 - 15th International Conference on Sampling Theory and Applications (SampTA 2025)

Y2 - 28 July 2025 through 1 August 2025

ER -

Wavelets on Intervals for Image Denoising

Abstract

Publication series

Conference

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

GRF: Graph Framelets for Graph Deep Learning: Homophily and Heterophily

ITF: Artificial Intelligence Methods and Applications for Breast Cancer Diagnosis and Treatment in Clinical Trials

GRF: Framelets for Geometric Deep Learning: Spheres, Graphs, and Neural Networks

Cite this

Wavelets on Intervals for Image Denoising

Abstract

Publication series

Conference

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Projects

GRF: Graph Framelets for Graph Deep Learning: Homophily and Heterophily

ITF: Artificial Intelligence Methods and Applications for Breast Cancer Diagnosis and Treatment in Clinical Trials

GRF: Framelets for Geometric Deep Learning: Spheres, Graphs, and Neural Networks

Cite this