Image analysis using a dual-tree M-band wavelet transform

Abstract : We propose a two-dimensional generalization to the M-band case of the dual-tree decomposition structure (initially proposed by Kingsbury and further investigated by Selesnick) based on a Hilbert pair of wavelets. We particularly address: 1) the construction of the dual basis and 2) 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, L. Duval, J.-C. Pesquet. Image analysis using a dual-tree M-band wavelet transform. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2006, 15 (8), pp.2397-2412. ⟨http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4567640&abstractAccess=no&userType=inst⟩. ⟨10.1109/TIP.2006.875178⟩. ⟨hal-01330599⟩

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