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

Authors:
C. Chaux;L. Duval;J. -C. Pesquet
Affiliations:
Inst. Gaspard Monge, Univ. de Marne-la-Vallee, France;-;-
Venue:
IEEE Transactions on Image Processing
Year:
2006

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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.