A new map estimator for wavelet domain image denoising using vector-based hidden Markov model

There are a number of image denoising methods in the wavelet domain using statistical models. It is known that the performance of such methods can be significantly improved by taking into account the statistical dependencies between the wavelet coefficients. It is shown that the vector-based hidden Markov model (VB-HMM) is capable of capturing both the subband marginal distribution and the inter-scale, intra-scale and cross orientation dependencies of the wavelet coefficients. In view of this, we propose a new maximum a posteriori estimator using the VB-HMM as a prior for the wavelet coefficients of images. This is realized by deriving an efficient closed-form expression for the shrinkage function. Experimental results are performed to evaluate the performance of the proposed denoising method. The results demonstrate that the proposed method outperforms some of the state-of-the-art techniques in terms of both the peak signal to noise ratio and perceptual quality.

I. Introduction

Image denoising can be regarded as a problem of estimating the clean image from noisy observations. There have been a number of works on image denoising especially in transform domain in that the wavelet transform has been successfully applied due to its properties such as locality, multi-resolution and compression. In recent works, the wavelet coefficient dependencies have been taken into account. In [1], a framework for statistical signal processing based on wavelet-domain hidden Markov model has been developed. In [2], an estimation-quantization algorithm has been proposed to consider the local dependencies of the wavelet coefficients employed in a locally adaptive window-based denoising technique. In [3], a neighboring wavelet thresholding has been used in the multiwavelet framework. In [4] and [5], a bivariate shrinkage function has been proposed for image denoising purpose considering the parent to child dependencies of the wavelet coefficients. In [6], an image denoising algorithm based on a Gaussian scale mixture model has been proposed in which the covariances between neighbor coefficients have been considered as the dependencies. The multivariate generalized Gaussian distribution has been introduced in [7] to exploit the coefficients dependencies across scales. A thresholding technique incorporating neighboring coefficients of the translation-invariant wavelet transform has been developed in [8]. In [9], a wavelet shrinkage function has been obtained using neighbor and level dependencies. The three-scale dependency of wavelet coefficients has been considered for a denoising scheme [10].