Open Access

Iterative Estimation Algorithms Using Conjugate Function Lower Bound and Minorization-Maximization with Applications in Image Denoising

EURASIP Journal on Advances in Signal Processing20082008:429128

https://doi.org/10.1155/2008/429128

Received: 19 September 2007

Accepted: 11 February 2008

Published: 24 February 2008

Abstract

A fundamental problem in signal processing is to estimate signal from noisy observations. This is usually formulated as an optimization problem. Optimizations based on variational lower bound and minorization-maximization have been widely used in machine learning research, signal processing, and statistics. In this paper, we study iterative algorithms based on the conjugate function lower bound (CFLB) and minorization-maximization (MM) for a class of objective functions. We propose a generalized version of these two algorithms and show that they are equivalent when the objective function is convex and differentiable. We then develop a CFLB/MM algorithm for solving the MAP estimation problems under a linear Gaussian observation model. We modify this algorithm for wavelet-domain image denoising. Experimental results show that using a single wavelet representation the performance of the proposed algorithms makes better than that of the bishrinkage algorithm which is arguably one of the best in recent publications. Using complex wavelet representations, the performance of the proposed algorithm is very competitive with that of the state-of-the-art algorithms.

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Authors’ Affiliations

(1)
Department of Electronic Engineering, La Trobe University
(2)
Department of Information Engineering, The Chinese University of Hong Kong

Copyright

© G. Deng and W.-Y. Ng. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.