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Istituto di Scienza e Tecnologie dell'Informazione     
Achim A., Kuruoglu E. E., Bezerianos A., Tsakalides P. A closed-form nonparametric Bayesian estimator in the wavelet domain of images using an approximate alpha-stable prior - Comment. In: Pattern Recognition Letters, vol. 28 (13) pp. 1845 - 1847. Elsevier, 2007.
 
 
Abstract
(English)
The purpose of this commentary is to point out that the paper by Boubchir and Fadili (B-F) [Boubchir, L., Fadili, J.M., 2006. A closedform nonparametric Bayesian estimator in the wavelet domain of images using an approximate alpha-stable prior. Pattern Recognit. Lett. 27, 1370-1382] is little more than a paraphrase of earlier work in [Achim, A., Bezerianos, A., Tsakalides, P., 2001. Novel Bayesian multiscale method for speckle removal in medical ultrasound images. IEEE Trans. Med. Imag. 20 (August), 772-783; Kuruoglu, E.E., Molina, C., Fitzgerald, W.J., 1998. Approximation of a-stable probability densities using finite Gaussian mixtures. In: Proc. EUSIPCO'98 (September); Portilla, J., Strela, V., Wainwright, M.J., Simoncelli, E.P., 2003. Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE. Trans. Image. Proc. 12 (November), 1338-1351]. Essentially, B-F purport to propose an algorithm for image denoising based on scale mixtures of Gaussians in the wavelet domain, an approach well documented in [Portilla, J., Strela, V., Wainwright, M.J., Simoncelli, E.P., 2003. Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE. Trans. Image. Proc. 12 (November), 1338-1351]. In achieving this, B-F make use of a known method for approximating alpha-stable distributions previously proposed by Kuruoglu and co-workers [Kuruoglu, E.E., 1998. Signal processing in alpha-stable noise environments:Aleast lp-norm approach. Ph.D. thesis, University of Cambridge, Cambridge; Kuruoglu, E.E., Molina, C., Fitzgerald, W.J., 1998. Approximation of alpha-stable probability densities using finite Gaussian mixtures. In: Proc. USIPCO'98 (September)], but without referring to their work. Together, the above observations do not entitle B-F to claim to have developed a new algorithm. In addition, we show that B-F [2006; Fadili, J.M., Boubchir, L., 2005. Analytical form for a Bayesian wavelet estimator of images using the Bessel K form densities. IEEE Trans. Image Process. 14 (2), 231-240] include unfair comments and comparison vis-a`-vis of the method proposed in our early work [Achim, A., Bezerianos, A., Tsakalides, P., 2001. Novel Bayesian multiscale method for speckle removal in medical ultrasound images. IEEE Trans. Med. Imag. (August) 20, 772-783].
Subject Alpha-stable distribution
Wavelet transform
Bayesian estimation
I.4.10 Image Representation. Hierarchical
I.4.10 Image Representation. Statistical
G.3 Proability and Statistics. Distribution functions
42C40 Wavelets
62H35 Image analysis
62H10 Distribution of statistics
60E07 Infinitely divisible distributions; stable distributions


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