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.
Cite
@article{arxiv.2103.15674,
title = {4D Dual-Tree Complex Wavelets for Time-Dependent Data},
author = {Tatiana A. Bubba and Tommi Heikkilä and Samuli Siltanen},
journal= {arXiv preprint arXiv:2103.15674},
year = {2023}
}