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

The dual-tree complex wavelet transform (DT-\(\mathbb{C}\)WT) is extended to the 4D setting. Key properties of 4D DT-\(\mathbb{C}\)WT, such as directional sensitivity and shift-invariance, are discussed and illustrated in a tomographic application. The inverse problem of reconstructing a dynamic thr...

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Bibliographic Details
Published in:arXiv.org 2021-03
Main Authors: Bubba, Tatiana A, Heikkilä, Tommi, Siltanen, Samuli
Format: Article
Language:English
Subjects:
Directional sensitivity
Inverse problems
Time dependence
Wavelet transforms
Online Access:Get full text
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Summary:The dual-tree complex wavelet transform (DT-\(\mathbb{C}\)WT) is extended to the 4D setting. Key properties of 4D DT-\(\mathbb{C}\)WT, 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-\(\mathbb{C}\)WT offers simple implementations combined with useful theoretical properties for tomographic reconstruction.
ISSN:2331-8422
DOI:10.48550/arxiv.2103.15674