4D Dual-Tree Complex Wavelets for Time-Dependent Data

Tatiana Bubba; Tommi Heikkilä; Samuli Siltanen

doi:10.1109/ICCSA54496.2021.00029

4D Dual-Tree Complex Wavelets for Time-Dependent Data

Tatiana Bubba, Tommi Heikkilä, Samuli Siltanen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

Abstract

The dual-tree complex wavelet transform (DT-ℂWT) is extended to the 4D setting. Key properties of 4D DT-ℂWT, such as directional sensitivity and shift-invariance, are discussed and illustrated in a tomographic application. The inverse problem of reconstructing a dynamic three-dimensional target from X-ray projection measurements can be formulated as 4D space-time tomography. The results suggest that 4D DT-ℂWT offers simple implementations combined with useful theoretical properties for tomographic reconstruction.

Original language	English
Title of host publication	2021 21st International Conference on Computational Science and Its Applications (ICCSA) : Workshop Computational and Applied Mathematics (CAM 2021)
Number of pages	11
Publisher	IEEE
Publication date	16 Mar 2022
Pages	146-156
ISBN (Print)	978-1-6654-5844-3
ISBN (Electronic)	978-1-6654-5843-6
DOIs	https://doi.org/10.1109/ICCSA54496.2021.00029
Publication status	Published - 16 Mar 2022
MoE publication type	A4 Article in conference proceedings
Event	International Conference on Computational Science and Its Applications – ICCSA 2021 - University of Cagliari, Cagliari, Italy Duration: 13 Sept 2021 → 16 Sept 2021

Fields of Science

111 Mathematics
COMPLEX WAVELETS
Dynamic tomography

Access to Document

10.1109/ICCSA54496.2021.00029

4D_Dual_Tree_Complex_Wavelets_for_Time_Dependent_Data_2Accepted author manuscript, 792 KBLicence: Unspecified

https://arxiv.org/abs/2103.15674Licence: CC BY

Cone-beam gel phatom data for dynamic X-ray tomography
Heikkilä, T. (Creator), Meaney, A. (Creator) & Help-Rinta-Rahko, H. (Creator), Zenodo, 28 Apr 2023
DOI: 10.5281/zenodo.7739985
Dataset

Cite this

@inproceedings{0e403bd12be44d8887bfdff9b6ad8f30,

title = "4D Dual-Tree Complex Wavelets for Time-Dependent Data",

abstract = "The dual-tree complex wavelet transform (DT-ℂWT) is extended to the 4D setting. Key properties of 4D DT-ℂWT, such as directional sensitivity and shift-invariance, are discussed and illustrated in a tomographic application. The inverse problem of reconstructing a dynamic three-dimensional target from X-ray projection measurements can be formulated as 4D space-time tomography. The results suggest that 4D DT-ℂWT offers simple implementations combined with useful theoretical properties for tomographic reconstruction.",

keywords = "111 Mathematics, COMPLEX WAVELETS, Dynamic tomography, COMPLEX WAVELETS, Dynamic tomography",

author = "Tatiana Bubba and Tommi Heikkil{\"a} and Samuli Siltanen",

year = "2022",

month = mar,

day = "16",

doi = "10.1109/ICCSA54496.2021.00029",

language = "English",

isbn = "978-1-6654-5844-3",

pages = "146--156",

booktitle = "2021 21st International Conference on Computational Science and Its Applications (ICCSA)",

publisher = "IEEE",

address = "Italy",

note = "International Conference on Computational Science and Its Applications – ICCSA 2021, ICCSA 2021 ; Conference date: 13-09-2021 Through 16-09-2021",

}

Bubba, T , Heikkilä, T & Siltanen, S 2022, 4D Dual-Tree Complex Wavelets for Time-Dependent Data. in 2021 21st International Conference on Computational Science and Its Applications (ICCSA): Workshop Computational and Applied Mathematics (CAM 2021). IEEE, pp. 146-156, International Conference on Computational Science and Its Applications – ICCSA 2021, Cagliari, Italy, 13/09/2021. https://doi.org/10.1109/ICCSA54496.2021.00029

4D Dual-Tree Complex Wavelets for Time-Dependent Data. / Bubba, Tatiana ; Heikkilä, Tommi ; Siltanen, Samuli.
2021 21st International Conference on Computational Science and Its Applications (ICCSA): Workshop Computational and Applied Mathematics (CAM 2021). IEEE, 2022. p. 146-156.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

TY - GEN

T1 - 4D Dual-Tree Complex Wavelets for Time-Dependent Data

AU - Bubba, Tatiana

AU - Heikkilä, Tommi

AU - Siltanen, Samuli

PY - 2022/3/16

Y1 - 2022/3/16

N2 - The dual-tree complex wavelet transform (DT-ℂWT) is extended to the 4D setting. Key properties of 4D DT-ℂWT, such as directional sensitivity and shift-invariance, are discussed and illustrated in a tomographic application. The inverse problem of reconstructing a dynamic three-dimensional target from X-ray projection measurements can be formulated as 4D space-time tomography. The results suggest that 4D DT-ℂWT offers simple implementations combined with useful theoretical properties for tomographic reconstruction.

AB - The dual-tree complex wavelet transform (DT-ℂWT) is extended to the 4D setting. Key properties of 4D DT-ℂWT, such as directional sensitivity and shift-invariance, are discussed and illustrated in a tomographic application. The inverse problem of reconstructing a dynamic three-dimensional target from X-ray projection measurements can be formulated as 4D space-time tomography. The results suggest that 4D DT-ℂWT offers simple implementations combined with useful theoretical properties for tomographic reconstruction.

KW - 111 Mathematics

KW - COMPLEX WAVELETS

KW - Dynamic tomography

KW - COMPLEX WAVELETS

KW - Dynamic tomography

U2 - 10.1109/ICCSA54496.2021.00029

DO - 10.1109/ICCSA54496.2021.00029

M3 - Conference contribution

SN - 978-1-6654-5844-3

SP - 146

EP - 156

BT - 2021 21st International Conference on Computational Science and Its Applications (ICCSA)

PB - IEEE

T2 - International Conference on Computational Science and Its Applications – ICCSA 2021

Y2 - 13 September 2021 through 16 September 2021

ER -

4D Dual-Tree Complex Wavelets for Time-Dependent Data

Abstract

Fields of Science

Access to Document

Datasets

Cone-beam gel phatom data for dynamic X-ray tomography

Cite this