title: 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.
authors.affiliation: Institut Gaspard Monge and CNRS-UMR 8049, Université de Marne-la-Vallée, 77454 Marne-la-Vallée Cedex 2, France. chaux@univ-mlv.fr
authors.forename: Caroline
authors.initials: C
authors.lastname: Chaux
authors.forename: Laurent
authors.initials: L
authors.lastname: Duval
authors.forename: Jean-Christophe
authors.initials: JC
authors.lastname: Pesquet
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*; D012815:Signal Processing, Computer-Assisted