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

TL;DR

This paper extends the dual-tree complex wavelet transform to four dimensions, demonstrating its advantages in time-dependent data analysis and tomographic reconstruction with properties like directional sensitivity and shift-invariance.

Contribution

The paper introduces a 4D dual-tree complex wavelet transform, highlighting its theoretical properties and practical application in 4D space-time tomography.

Findings

Enhanced directional sensitivity in 4D wavelet transform

Shift-invariance in 4D DT-Complex Wavelets

Effective application to 4D tomographic reconstruction

Abstract

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.