Image analysis using a dual-tree M-band wavelet transform
- 17 July 2006
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Image Processing
- Vol. 15 (8), 2397-2412
- https://doi.org/10.1109/tip.2006.875178
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.Keywords
This publication has 28 references indexed in Scilit:
- The Double-Density Dual-Tree DWTIEEE Transactions on Signal Processing, 2004
- On the phase condition and its solution for hilbert transform pairs of wavelet basesIEEE Transactions on Signal Processing, 2003
- The design of approximate Hilbert transform pairs of wavelet basesIEEE Transactions on Signal Processing, 2002
- Discrete wavelet transform implementation in Fourier domain for multidimensional signalJournal of Electronic Imaging, 2002
- Lattice structure for regular paraunitary linear-phase filterbanks and M-band orthogonal symmetric waveletsIEEE Transactions on Signal Processing, 2001
- Linear-phase perfect reconstruction filter bank: lattice structure, design, and application in image codingIEEE Transactions on Signal Processing, 2000
- Time-invariant orthonormal wavelet representationsIEEE Transactions on Signal Processing, 1996
- Adapting to Unknown Smoothness via Wavelet ShrinkageJournal of the American Statistical Association, 1995
- Design of efficient M-band coders with linear-phase and perfect-reconstruction propertiesIEEE Transactions on Signal Processing, 1995
- Theory of regular M-band wavelet basesIEEE Transactions on Signal Processing, 1993