Application of Gaussian mixture field and wavelet-domain hidden Markov model to medical image denoising

Abstract

In this paper, we propose a new Wavelet-domain Hidden Markov Model (WHMM) for image denoising, which can exploit the local statistics and also capture intra-scale dependencies of the wavelet coefficients. Firstly, a Gaussian Mixture Field (GMF) on the wavelet transform is developed. In the GMF, we assume each wavelet coefficient follows a local Gaussian Mixture Model (GMM) which is determined by its own neighborhood. The GMF contains rich local statistics of wavelet coefficients, which can be further combined with the contextual WHMM (CWHMM) to capture inter-scale or intra-scale dependencies. Based on our numerous simulation results, we find that the combination of the GMF and the inter-scale CWHMIM performs better than the combination of the GMF and the intra-scale CWHMM. We also notice that there is no significant benefit to consider both the inter-scale and intra-scale dependencies together in the GMF. Therefore, for the simplification of implementation, we consider the combination of the GMF and the intra-scale CWIHMM and name the novel model Gaussian Mixture Field Wavelet-domain Hidden Markov Model (GMFWWVIIM) in this work. The newly proposed GMFWHMM allows more accurate image modeling with improved denoising performance at the low computational complexity. Finally, the novel model is applied to medical image denoising with interesting results.