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arXiv · 1702.08534

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

Caroline Chaux·Laurent Duval·Jean-Christophe Pesquet
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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.

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Caroline Chaux, Laurent Duval, Jean-Christophe Pesquet. 2017-02-27. Image Analysis Using a Dual-Tree $M$-Band Wavelet Transform. https://doi.org/10.1109/tip.2006.875178

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