Denoising model for parallel magnetic resonance imaging images using higher‐order Markov random fields. Issue 12 (1st December 2016) - Xu, Zhihuo; Shi, Quan
Abstract : This study presents a novel robust method for Bayesian denoising of parallel magnetic resonance imaging (pMRI) images. For the first time, the authors' proposal applies fields of experts (FoE), a filter‐based higher‐order Markov random field (MRF), to model the prior of the pMRI image statistics. The noise in pMRI data behaves to be non‐central Chi (nc‐ χ ) distributed. In practice, correlation between coils exists, resulting in that nc‐ χ distribution does not hold anymore and the spatially varying noise problem. Thus, preservation of fine textures requires to adapt locally the estimation. Therefore, more precisely, the noise is reduced by using a sliding window scheme. In each window, the likelihood probability function is accurately modelled from corrupted data by using an innovative Gaussian mixture model (GMM). The parameters of GMM are calculated by applying an iterative expectation maximisation approach. With the priors via the learned FoE model and the likelihood function via GMM, a maximum a posteriori (MAP) estimator is formulated. Then, the noise in the each window is filtered by applying an efficient non‐linear quasi‐Newton method to explore an optimal solution for the MAP estimator. Finally, experiments have been conducted on both the simulated and real data to compare the proposed model with some state‐of‐the‐art denoising methods. The experimental results demonstrate the robustness and effectiveness of the proposed denoising model.