20 September 2007 Modeling statistical properties of wavelets using a mixture of bivariate cauchy models and its application for image denoising in complex wavelet domain
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Abstract
In this paper, we design a bivariate maximum a posteriori (MAP) estimator that supposes the prior of wavelet coefficients as a mixture of bivariate Cauchy distributions. This model not only is a mixture but is also bivariate. Since mixture models are able to capture the heavy-tailed property of wavelets and bivaraite distributions can model the intrascale dependences of wavelet coefficients, this bivariate mixture probability density function (pdf) can better capture statistical properties of wavelet coefficients. The simulation results show that our proposed technique achieves better performance than other methods employing non mixture pdfs such as bivariate Cauchy pdf and circular symmetric Laplacian pdf visually and in terms of peak signal-to-noise ratio (PSNR). We also compare our algorithm with several recently published denoising methods and see that it is among the best reported in the literature.
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Hossein Rabbani, Hossein Rabbani, Mansur Vafadust, Mansur Vafadust, Ivan Selesnick, Ivan Selesnick, } "Modeling statistical properties of wavelets using a mixture of bivariate cauchy models and its application for image denoising in complex wavelet domain", Proc. SPIE 6701, Wavelets XII, 67012I (20 September 2007); doi: 10.1117/12.739253; https://doi.org/10.1117/12.739253
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