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access icon free Denoising model for parallel magnetic resonance imaging images using higher-order Markov random fields

© The Institution of Engineering and Technology
Received 05/03/2016, Accepted 16/07/2016, Revised 23/06/2016, Published 19/07/2016

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.

Inspec keywords: Gaussian processes; expectation-maximisation algorithm; medical image processing; image denoising; biomedical MRI; Markov processes; mixture models; statistical distributions; image texture

Other keywords: sliding window scheme; iterative expectation maximisation approach; MAP estimator; fields-of-experts; texture preservation; Bayesian denoising model; maximum-a-posteriori estimator; pMRI image statistics; likelihood probability function; nonlinear quasi Newton method; MRF; FoE model; Gaussian mixture model; GMM; filter-based higher-order Markov random field; noncentral Chi distribution; parallel magnetic resonance imaging images

Subjects: Markov processes; Optical, image and video signal processing; Patient diagnostic methods and instrumentation; Interpolation and function approximation (numerical analysis); Numerical approximation and analysis; Biomedical magnetic resonance imaging and spectroscopy; Biology and medical computing; Markov processes; Interpolation and function approximation (numerical analysis); Probability theory, stochastic processes, and statistics; Medical magnetic resonance imaging and spectroscopy; Computer vision and image processing techniques

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