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Noise Covariance Properties in Dual-Tree Wavelet Decompositions.
- Source :
- IEEE Transactions on Information Theory; Dec2007, Vol. 53 Issue 12, p4680-4700, 21p, 2 Diagrams, 9 Charts
- Publication Year :
- 2007
-
Abstract
- Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is performed—which occurs in particular when an additive noise is corrupting the signal to be analyzed—it is useful to characterize the statistical properties of the dual-tree wavelet coefficients of this process. As dual-tree decompositions constitute overcomplete frame expansions, correlation structures are introduced among the coefficients, even when a white noise is analyzed. In this paper, we show that it is possible to provide an accurate description of the covariance properties of the dual-tree coefficients of a wide-sense-stationary process. The expressions of the (cross-) covariance sequences of the coefficients are derived in the one- and two-dimensional cases. Asymptotic results are also provided, allowing to predict the behavior of the second-order moments for large lag values or at coarse resolution. In addition, the cross-correlations between the primal and dual wavelets, which play a primary role in our theoretical analysis, are calculated for a number of classical wavelet families. Simulation results are finally provided to validate these results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 53
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 28439030
- Full Text :
- https://doi.org/10.1109/TIT.2007.909104