Improve maximum likelihood estimation for subband GGD parameters

Statistical model of subband wavelet coefficients fitted with generalized Gaussian density (GGD) has been widely used into image retrieval, classification, segmentation, denoising, and analysis/synthesis. Moment estimation is very simple method for estimation of the GGD parameters, but it is not sharp. Maximum likelihood estimation is obtained by solving the transcendental equation. Unfortunately, the equation has not analytical solution, and has to be solved numerically. We discover that Newton-Raphson iteration converges very slowly for the transcendental equation. To speed up convergence, we present Regula-Falsi method in place of Newton-Raphson method. The experiments show that Regula-Falsi method reaches the accuracy of the order 10^-^7 in three iterations.

[1]  Shih-Fu Chang,et al.  Transform features for texture classification and discrimination in large image databases , 1994, Proceedings of 1st International Conference on Image Processing.

[2]  Michael Unser,et al.  Texture classification and segmentation using wavelet frames , 1995, IEEE Trans. Image Process..

[3]  Paul Scheunders,et al.  Statistical texture characterization from discrete wavelet representations , 1999, IEEE Trans. Image Process..

[4]  Jian Fan,et al.  Texture Classification by Wavelet Packet Signatures , 1993, MVA.

[5]  Asoke K. Nandi,et al.  Exponent parameter estimation for generalized Gaussian probability density functions with application to speech modeling , 2005, Signal Process..

[6]  Alberto Leon-Garcia,et al.  Estimation of shape parameter for generalized Gaussian distributions in subband decompositions of video , 1995, IEEE Trans. Circuits Syst. Video Technol..

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

[8]  J. Bergen,et al.  Pyramid-based texture analysis/synthesis , 1995, Proceedings., International Conference on Image Processing.

[9]  Minh N. Do,et al.  Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance , 2002, IEEE Trans. Image Process..

[10]  C.-C. Jay Kuo,et al.  Texture analysis and classification with tree-structured wavelet transform , 1993, IEEE Trans. Image Process..

[11]  A. Ralston.  A first course in numerical analysis , 1965 .

[12]  Pierre Moulin,et al.  Analysis of Multiresolution Image Denoising Schemes Using Generalized Gaussian and Complexity Priors , 1999, IEEE Trans. Inf. Theory.

[13]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Luciano Alparone,et al.  Estimation based on entropy matching for generalized Gaussian PDF modeling , 1999, IEEE Signal Processing Letters.

[15]  Xiang-Gen Xia,et al.  Improved hidden Markov models in the wavelet-domain , 2001, IEEE Trans. Signal Process..