Image Analysis Using a Dual-Tree $M$-Band Wavelet Transform

TL;DR

This paper introduces a new 2D dual-tree M-band wavelet transform for image analysis, enhancing directional features and denoising performance through an optimal reconstruction method, demonstrated on various image types.

Contribution

It extends the dual-tree wavelet framework to M-band case with a novel construction and an optimal reconstruction technique for improved image denoising.

Findings

Enhanced noise reduction in images

Better directional feature preservation

Improved denoising across different image types

Abstract

We propose a 2D generalization to the $M$-band case of the dual-tree decomposition structure (initially proposed by N. Kingsbury and further investigated by I. Selesnick) based on a Hilbert pair of wavelets. We particularly address (\textit{i}) the construction of the dual basis and (\textit{ii}) the resulting directional analysis. We also revisit the necessary pre-processing stage in the $M$-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed $M$-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various $M$-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.