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

By Chaux & Duval & Pesquet

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 (i) the
construction of the dual basis and (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. Signicant improvements
in terms of both overall noise reduction and direction
preservation are observed.

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