EURASIP Journal on Advances in Signal Processing 
Volume 2008 (2008), Article ID 429128, 12 pages
doi:10.1155/2008/429128
Research Article

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

Guang Deng1 and Wai-Yin Ng2

 1Department of Electronic Engineering, La Trobe University, Bundoora, Victoria 3086, Australia
2Department of Information Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong
Received 19 September 2007; Revised 3 January 2008; Accepted 11 February 2008

Recommended by Hubert Cardot

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.