Image denoising using bivariate α-stable distributions in the complex wavelet domain

Recently, the dual-tree complex wavelet transform has been proposed as an analysis tool featuring near shift-invariance and improved directional selectivity compared to the standard wavelet transform. Within this framework, we describe a novel technique for removing noise from digital images. We design a bivariate maximum a posteriori estimator, which relies on the family of isotropic α-stable distributions. Using this relatively new statistical model we are able to better capture the heavy-tailed nature of the data as well as the interscale dependencies of wavelet coefficients. We test our algorithm for the Cauchy case, in comparison with several recently published methods. The simulation results show that our proposed technique achieves state-of-the-art performance in terms of root mean squared (RMS) error.

[1]  I. Selesnick,et al.  Bivariate shrinkage with local variance estimation , 2002, IEEE Signal Processing Letters.

[2]  N. Kingsbury Complex Wavelets for Shift Invariant Analysis and Filtering of Signals , 2001 .

[3]  M. Taqqu,et al.  Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance , 1995 .

[4]  Dimitrios Hatzinakos,et al.  Applications of the empirical characteristic function to estimation and detection problems , 1998, Signal Process..

[5]  Robert D. Nowak,et al.  Wavelet-based statistical signal processing using hidden Markov models , 1998, IEEE Trans. Signal Process..

[6]  Chrysostomos L. Nikias,et al.  Scalar quantisation of heavy-tailed signals , 2000 .

[7]  Martin J. Wainwright,et al.  Image denoising using scale mixtures of Gaussians in the wavelet domain , 2003, IEEE Trans. Image Process..

[8]  Alin Achim,et al.  Astrophysical image denoising using bivariate isotropic Cauchy distributions in the undecimated wavelet domain , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[9]  J. Nolan,et al.  Multivariate stable distributions: approximation, estimation, simulation and identification , 1998 .

[10]  竹中 茂夫 G.Samorodnitsky,M.S.Taqqu:Stable non-Gaussian Random Processes--Stochastic Models with Infinite Variance , 1996 .

[11]  Alin Achim,et al.  Novel Bayesian multiscale method for speckle removal in medical ultrasound images , 2001, IEEE Transactions on Medical Imaging.

[12]  N. Kingsbury Image processing with complex wavelets , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[13]  Aleksandra Pizurica,et al.  A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising , 2002, IEEE Trans. Image Process..

[14]  William J. Fitzgerald,et al.  Approximation of α-stable probability densities using finite Gaussian mixtures , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[15]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[16]  Alin Achim,et al.  SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling , 2003, IEEE Trans. Geosci. Remote. Sens..

[17]  Levent Sendur,et al.  Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency , 2002, IEEE Trans. Signal Process..

[18]  C. L. Nikias,et al.  Signal processing with alpha-stable distributions and applications , 1995 .