%0 Journal Article %T Image analysis using a dual-tree M-band wavelet transform %+ Laboratoire d'Informatique Gaspard-Monge (LIGM) %+ IFP Energies nouvelles (IFPEN) %A Chaux, Caroline %A Duval, L. %A Pesquet, J.-C. %< avec comité de lecture %@ 1057-7149 %J IEEE Transactions on Image Processing %I Institute of Electrical and Electronics Engineers %V 15 %N 8 %P 2397-2412 %8 2006 %D 2006 %R 10.1109/TIP.2006.875178 %M 16900693 %K dual-tree M-band wavelet transform %K directional analysis %K denoising %K M -band wavelet transform %K dual-tree wavelet transform %K Hilbert transforms %K image denoising %K image reconstruction %K wavelet transforms %K Hilbert wavelet pair %K image analysis %K optimal signal reconstruction technique %K thresholding strategies %K dual-tree %K Filter bank %Z Computer Science [cs]/Signal and Image Processing %Z Computer Science [cs]/Computation and Language [cs.CL]Journal articles %X 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. %G English %2 https://ifp.hal.science/hal-01330599/document %2 https://ifp.hal.science/hal-01330599/file/Chaux_C_2006_tip_ima_adtmbwt-image-dual-tree-m-band.pdf %L hal-01330599 %U https://ifp.hal.science/hal-01330599 %~ ENPC %~ IFP %~ CNRS %~ UNIV-MLV %~ LIGM_SIGNAL %~ PARISTECH %~ ENPC-LIGM %~ LIGM %~ CV_LIGM %~ UNIV-EIFFEL %~ UPEM-UNIVEIFFEL %~ ESIEE-UNIVEIFFEL %~ TEST3-HALCNRS