A closed-form nonparametric Bayesian estimator in the wavelet domain of images using an approximate α-stable prior

摘要

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 closed-form nonparametric Bayesian estimator in the wavelet domain of images using an approximate α-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 α-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 α-stable distributions previously proposed by Kuruoglu and co-workers [Kuruoglu, E.E., 1998. Signal processing in α-stable noise environments: A least 1 p-norm approach. Ph.D. thesis, University of Cambridge, Cambridge; Kuruoglu, E.E., Molina, C, Fitzgerald, W.J., 1998. Approximation of α-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].