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

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Publication date: 27 February 2017

Abstract: We propose a 2D generalization to the

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-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 ( extit{i}) the construction of the dual basis and ( extit{ii}) the resulting directional analysis. We also revisit the necessary pre-processing stage in the

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-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

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-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various

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-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.

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