Noise Correction on Rician Distributed Data for Fibre Orientation Estimators

Abstract

New complex tissue microstructure estimators have been presented recently in order to elucidate white matter fibre orientations. Since these algorithms are based on the diffusion-weighted signal profile, the estimations are affected by noise artefacts. The proven robustness of these methods cannot counteract distortions since the statistical Rician behavior has not been taken into account. In this study, two techniques to counteract the noise distortions are presented to improve the fibre orientation estimations. Simulations and in vivo experiments show an improvement in the angular resolution and convergence of the results. One of these strategies represents a good compromise between computational cost and result improvements.

A Majorize-Minimize Framework for Rician and Non-Central Chi MR Images

“…This leads to phase inconsistencies for in vivo data. In addition, the physics of the diffusion encoding process also means that diffusion MR images typically have low-SNR [17], [19], [20], [24], [25]. This combination of characteristics means that PML-based NCC modeling should be particularly attractive.…”

Noise estimation in single- and multiple-coil magnetic resonance data based on statistical models

“…Due to these sources of error, it is advisable to use estimators in Eqs. (12) to (24) even when an automatic segmentation of the background is feasible. A robust estimation method would involve a rough automatic segmentation of the Rayleigh area -using for instance some thresholding method, as the ones proposed in Refs.…”

“…Many filtering methods to improve SNR in MRI need an estimated value for σ n 2 such as the conventional approach [11], maximum likelihood-based methods [12][13][14], expectation maximization formulations with Rician noise assumptions [15], linear minimum mean square error-based schemes [10,[16][17][18] and unbiased nonlocal mean schemes [19][20][21]. New techniques for DTI tensor estimation [22,23], segmentation methods based on the Rician distribution and fiber orientation estimators [24] also depend upon an estimated σ n 2 value. The aims of this article were (1) to review and classify different approaches to estimate noise in Rician magnitude MR images; (2) to propose new methods to estimate noise in magnitude images; (3) to extend the Rician-based estimators to the non-central chi model; and (4) to propose a method to estimate noise in complex MR images, if they are available.…”

Impact of Rician Adapted Non-Local Means Filtering on HARDI

“…In the context of diffusion tensor MRI (DTI), recent attempts have been made to account for the Rician noise to regularize the DW data [2], to estimate the diffusion tensor [3], or to perform both tasks simultaneously [4]. However, among the existing methods to estimate and/or regularize orientation distribution function (ODF) reconstructions from high angular resolution diffusion imaging (HARDI) [5,6,7,8], the Rician noise bias has just started to be addressed. In [5], local geometries of 3D curves are used in a relaxation labeling framework to regularize fields of DT and ODFs and show good results without modeling the Rician noise explicitly.…”

“…On the other hand, [6] uses a variational flow formulation to estimate a robust field of ODF that incorporates a possibly more complex noise distribution to account for the Rician bias. Other very recent attempts, similar in spirit to our approach because working directly on the raw DWI, includes the correction of the raw DWI signal [8] and inject a Rician statistics term in the iterative algorithm that reconstructs the fibre orientation density [8] or use a linear mean square error estimator that restores DWI using a Rician noise modeling [7].…”