Effective noise estimation and filtering from correlated multiple-coil MR data

MP-PCA denoising of fMRI time-series data can lead to artificial activation "spreading"

MP-PCA denoising has become the method of choice for denoising MRI data since it provides an objective threshold to separate the signal components from unwanted thermal noise components. In rodents, thermal noise in the coils is an important source of noise that can reduce the accuracy of activation mapping in fMRI. Further confounding this problem, vendor data often contains zero-filling and other post-processing steps that may violate MP-PCA assumptions. Here, we develop an approach to denoise vendor data and assess activation "spreading" caused by MP-PCA denoising in rodent task-based fMRI data. Data was obtained from N = 3 mice using conventional multislice and ultrafast acquisitions (1 s and 50 ms temporal resolution, respectively), during visual stimulation. MP-PCA denoising produced SNR gains of 64% and 39% and Fourier Spectral Amplitude (FSA) increases in BOLD maps of 9% and 7% for multislice and ultrafast data, respectively, when using a small [2 2] denoising window. Larger windows provided higher SNR and FSA gains with increased spatial extent of activation that may or may not represent real activation. Simulations showed that MP-PCA denoising can incur activation "spreading" with increased false positive rate and smoother functional maps due to local "bleeding" of principal components, and that the optimal denoising window for improved specificity of functional mapping, based on Dice score calculations, depends on the data's tSNR and functional CNR. This "spreading" effect applies also to another recently proposed low-rank denoising method (NORDIC), although to a lesser degree. Our results bode well for enhancing spatial and/or temporal resolution in future fMRI work, while taking into account the sensitivity/specificity trade-offs of low-rank denoising methods.

Comparison of two types of microscopic diffusion anisotropy in mouse brain

Two distinct types of microscopic diffusion anisotropy (MA) are compared in brain for both normal control and transgenic (3xTg-AD) mice, which develop Alzheimer's disease pathology. The first type of MA is the commonly used microscopic fractional anisotropy (μFA), and the second is a new MA measure referred to as μFA'. These two MA parameters have different symmetry properties that are central to their physical interpretations. Specifically, μFA is invariant with respect to local rotations of compartmental diffusion tensors while μFA' is invariant with respect to global diffusion tensor deformations. A key distinction between μFA and μFA' is that μFA is affected by the same type of orientationally coherent diffusion anisotropy as the conventional fractional anisotropy (FA) while μFA' is not. Furthermore, μFA can be viewed as having independent contributions from FA and μFA', as is quantified by an equation relating all three anisotropies. The normal control and transgenic mice are studied at ages ranging from 2 to 15 months, with double diffusion encoding MRI being used to estimate μFA and μFA'. μFA and μFA' are nearly identical in low FA brain regions, but they show notable differences when FA is large. In particular, μFA and FA are found to be strongly correlated in the fimbria, but μFA' and FA are not. In addition, both μFA and μFA' are seen to increase with age in the corpus callosum and external capsule, and modest differences between normal control and transgenic mice are observed for μFA and μFA' in the corpus callosum and for μFA in the fimbria. The triad of FA, μFA, and μFA' is proposed as a useful combination of parameters for assessing diffusion anisotropy in brain.

What's new and what's next in diffusion MRI preprocessing

Diffusion MRI (dMRI) provides invaluable information for the study of tissue microstructure and brain connectivity, but suffers from a range of imaging artifacts that greatly challenge the analysis of results and their interpretability if not appropriately accounted for. This review will cover dMRI artifacts and preprocessing steps, some of which have not typically been considered in existing pipelines or reviews, or have only gained attention in recent years: brain/skull extraction, B-matrix incompatibilities w.r.t the imaging data, signal drift, Gibbs ringing, noise distribution bias, denoising, between- and within-volumes motion, eddy currents, outliers, susceptibility distortions, EPI Nyquist ghosts, gradient deviations, B1 bias fields, and spatial normalization. The focus will be on "what's new" since the notable advances prior to and brought by the Human Connectome Project (HCP), as presented in the predecessing issue on "Mapping the Connectome" in 2013. In addition to the development of novel strategies for dMRI preprocessing, exciting progress has been made in the availability of open source tools and reproducible pipelines, databases and simulation tools for the evaluation of preprocessing steps, and automated quality control frameworks, amongst others. Finally, this review will consider practical considerations and our view on "what's next" in dMRI preprocessing.

The sensitivity of diffusion MRI to microstructural properties and experimental factors

Diffusion MRI is a non-invasive technique to study brain microstructure. Differences in the microstructural properties of tissue, including size and anisotropy, can be represented in the signal if the appropriate method of acquisition is used. However, to depict the underlying properties, special care must be taken when designing the acquisition protocol as any changes in the procedure might impact on quantitative measurements. This work reviews state-of-the-art methods for studying brain microstructure using diffusion MRI and their sensitivity to microstructural differences and various experimental factors. Microstructural properties of the tissue at a micrometer scale can be linked to the diffusion signal at a millimeter-scale using modeling. In this paper, we first give an introduction to diffusion MRI and different encoding schemes. Then, signal representation-based methods and multi-compartment models are explained briefly. The sensitivity of the diffusion MRI signal to the microstructural components and the effects of curvedness of axonal trajectories on the diffusion signal are reviewed. Factors that impact on the quality (accuracy and precision) of derived metrics are then reviewed, including the impact of random noise, and variations in the acquisition parameters (i.e., number of sampled signals, b-value and number of acquisition shells). Finally, yet importantly, typical approaches to deal with experimental factors are depicted, including unbiased measures and harmonization. We conclude the review with some future directions and recommendations on this topic.

Automated characterization of noise distributions in diffusion MRI data

Knowledge of the noise distribution in magnitude diffusion MRI images is the centerpiece to quantify uncertainties arising from the acquisition process. The use of parallel imaging methods, the number of receiver coils and imaging filters applied by the scanner, amongst other factors, dictate the resulting signal distribution. Accurate estimation beyond textbook Rician or noncentral chi distributions often requires information about the acquisition process (e.g., coils sensitivity maps or reconstruction coefficients), which is usually not available. We introduce two new automated methods using the moments and maximum likelihood equations of the Gamma distribution to estimate noise distributions as they explicitly depend on the number of coils, making it possible to estimate all unknown parameters using only the magnitude data. A rejection step is used to make the framework automatic and robust to artifacts. Simulations using stationary and spatially varying noncentral chi noise distributions were created for two diffusion weightings with SENSE or GRAPPA reconstruction and 8, 12 or 32 receiver coils. Furthermore, MRI data of a water phantom with different combinations of parallel imaging were acquired on a 3T Philips scanner along with noise-only measurements. Finally, experiments on freely available datasets from a single subject acquired on a 3T GE scanner are used to assess reproducibility when limited information about the acquisition protocol is available. Additionally, we demonstrated the applicability of the proposed methods for a bias correction and denoising task on an in vivo dataset acquired on a 3T Siemens scanner. A generalized version of the bias correction framework for non integer degrees of freedom is also introduced. The proposed framework is compared with three other algorithms with datasets from three vendors, employing different reconstruction methods. Simulations showed that assuming a Rician distribution can lead to misestimation of the noise distribution in parallel imaging. Results on the acquired datasets showed that signal leakage in multiband can also lead to a misestimation of the noise distribution. Repeated acquisitions of in vivo datasets show that the estimated parameters are stable and have lower variability than compared methods. Results for the bias correction and denoising task show that the proposed methods reduce the appearance of noise at high b-value. The proposed algorithms herein can estimate both parameters of the noise distribution automatically, are robust to signal leakage artifacts and perform best when used on acquired noise maps.

Computation of exact g-factor maps in 3D GRAPPA reconstructions

PURPOSE

To characterize the noise distributions in 3D-MRI accelerated acquisitions reconstructed with GRAPPA using an exact noise propagation analysis that operates directly in k-space.

THEORY AND METHODS

We exploit the extensive symmetries and separability in the reconstruction steps to account for the correlation between all the acquired k-space samples. Monte Carlo simulations and multi-repetition phantom experiments were conducted to test both the accuracy and feasibility of the proposed method; a high-resolution in-vivo experiment was performed to assess the applicability of our method to clinical scenarios.

RESULTS

Our theoretical derivation shows that the direct k-space analysis renders an exact noise characterization under the assumptions of stationarity and uncorrelation in the original k-space. Simulations and phantom experiments provide empirical support to the theoretical proof. Finally, the high-resolution in-vivo experiment demonstrates the ability of the proposed method to assess the impact of the sub-sampling pattern on the overall noise behavior.

CONCLUSIONS

By operating directly in the k-space, the proposed method is able to provide an exact characterization of noise for any Cartesian pattern sub-sampled along the two phase-encoding directions. Exploitation of the symmetries and separability into independent blocks through the image reconstruction procedure allows us to overcome the computational challenges related to the very large size of the covariance matrices involved.

Exact Calculation of Noise Maps and ${g}$ -Factor in GRAPPA Using a ${k}$ -Space Analysis

Characterization of the noise distribution in magnetic resonance images has multiple applications, including quality assurance and protocol optimization. Noise characterization is particularly important in the presence of parallel imaging acceleration with multi-coil acquisitions, where the noise distribution can contain severe spatial heterogeneities. If the parallel imaging reconstruction is a linear process, an accurate noise analysis can be carried out by taking into account the correlations between all the samples involved. However, for -space-based techniques such as generalized autocalibrating partially parallel acquisition (GRAPPA), the exact analysis has been considered computationally prohibitive due to the very large size of the noise covariance matrices required to characterize the noise propagation from -space to image space. Previously proposed methods avoid this computational burden by formulating the GRAPPA reconstruction as a pixel-wise linear operation performed in the image space. However, these methods are not exact in the presence of non-uniform sampling of -space (e.g., containing a calibration region). For this reason, in this paper, we develop an accurate characterization of the noise distribution for self-calibrated parallel imaging in the presence of arbitrary Cartesian sampling patterns. By exploiting the symmetries and separability in the noise propagation process, the proposed method is computationally efficient and does not require large matrices. Under the assumption of a fixed reconstruction kernel, this method provides the precise distribution of the noise variance for each coil's image. These coil-by-coil noise maps are subsequently combined according to the coil combination approach used in image reconstruction, and therefore can be applied with both complex coil combination and root-sum-of-squares approaches. In this paper, we present the proposed noise characterization method and compare it to previous techniques using Monte Carlo simulations as well as phantom acquisitions.

Non-Stationary Rician Noise Estimation in Parallel MRI Using a Single Image: A Variance-Stabilizing Approach

Parallel magnetic resonance imaging (pMRI) techniques have gained a great importance both in research and clinical communities recently since they considerably accelerate the image acquisition process. However, the image reconstruction algorithms needed to correct the subsampling artifacts affect the nature of noise, i.e., it becomes non-stationary. Some methods have been proposed in the literature dealing with the non-stationary noise in pMRI. However, their performance depends on information not usually available such as multiple acquisitions, receiver noise matrices, sensitivity coil profiles, reconstruction coefficients, or even biophysical models of the data. Besides, some methods show an undesirable granular pattern on the estimates as a side effect of local estimation. Finally, some methods make strong assumptions that just hold in the case of high signal-to-noise ratio (SNR), which limits their usability in real scenarios. We propose a new automatic noise estimation technique for non-stationary Rician noise that overcomes the aforementioned drawbacks. Its effectiveness is due to the derivation of a variance-stabilizing transformation designed to deal with any SNR. The method was compared to the main state-of-the-art methods in synthetic and real scenarios. Numerical results confirm the robustness of the method and its better performance for the whole range of SNRs.

Validation of DWI pre-processing procedures for reliable differentiation between human brain gliomas

Diffusion magnetic resonance imaging (dMRI) is a powerful tool in clinical applications, in particular, in oncology screening. dMRI demonstrated its benefit and efficiency in the localisation and detection of different types of human brain tumours. Clinical dMRI data suffer from multiple artefacts such as motion and eddy-current distortions, contamination by noise, outliers etc. In order to increase the image quality of the derived diffusion scalar metrics and the accuracy of the subsequent data analysis, various pre-processing approaches are actively developed and used. In the present work we assess the effect of different pre-processing procedures such as a noise correction, different smoothing algorithms and spatial interpolation of raw diffusion data, with respect to the accuracy of brain glioma differentiation. As a set of sensitive biomarkers of the glioma malignancy grades we chose the derived scalar metrics from diffusion and kurtosis tensor imaging as well as the neurite orientation dispersion and density imaging (NODDI) biophysical model. Our results show that the application of noise correction, anisotropic diffusion filtering, and cubic-order spline interpolation resulted in the highest sensitivity and specificity for glioma malignancy grading. Thus, these pre-processing steps are recommended for the statistical analysis in brain tumour studies.

Effects of RF pulse profile and intra-voxel phase dispersion on MR fingerprinting with balanced SSFP readout

PURPOSE

To investigate possible errors in T1 and T2 quantification via MR fingerprinting with balanced steady-state free precession readout in the presence of intra-voxel phase dispersion and RF pulse profile imperfections, using computer simulations based on Bloch equations.

MATERIALS AND METHODS

A pulse sequence with TR changing in a Perlin noise pattern and a nearly sinusoidal pattern of flip angle following an initial 180-degree inversion pulse was employed. Gaussian distributions of off-resonance frequency were assumed for intra-voxel phase dispersion effects. Slice profiles of sinc-shaped RF pulses were computed to investigate flip angle profile influences. Following identification of the best fit between the acquisition signals and those established in the dictionary based on known parameters, estimation errors were reported. In vivo experiments were performed at 3T to examine the results.

RESULTS

Slight intra-voxel phase dispersion with standard deviations from 1 to 3Hz resulted in prominent T2 under-estimations, particularly at large T2 values. T1 and off-resonance frequencies were relatively unaffected. Slice profile imperfections led to under-estimations of T1, which became greater as regional off-resonance frequencies increased, but could be corrected by including slice profile effects in the dictionary. Results from brain imaging experiments in vivo agreed with the simulation results qualitatively.

CONCLUSION

MR fingerprinting using balanced SSFP readout in the presence of intra-voxel phase dispersion and imperfect slice profile leads to inaccuracies in quantitative estimations of the relaxation times.

Noise Estimation and Reduction in Magnetic Resonance Imaging Using a New Multispectral Nonlocal Maximum-likelihood Filter

Denoising of magnetic resonance (MR) images enhances diagnostic accuracy, the quality of image manipulations such as registration and segmentation, and parameter estimation. The first objective of this paper is to introduce a new, high-performance, nonlocal filter for noise reduction in MR image sets consisting of progressively-weighted, that is, multispectral, images. This filter is a multispectral extension of the nonlocal maximum likelihood filter (NLML). Performance was evaluated on synthetic and in-vivo T₂ - and T₁ -weighted brain imaging data, and compared to the nonlocal-means (NLM) and its multispectral version, that is, MS-NLM, and the nonlocal maximum likelihood (NLML) filters. Visual inspection of filtered images and quantitative analyses showed that all filters provided substantial reduction of noise. Further, as expected, the use of multispectral information improves filtering quality. In addition, numerical and experimental analyses indicated that the new multispectral NLML filter, MS-NLML, demonstrated markedly less blurring and loss of image detail than seen with the other filters evaluated. In addition, since noise standard deviation (SD) is an important parameter for all of these nonlocal filters, a multispectral extension of the method of maximum likelihood estimation (MLE) of noise amplitude is presented and compared to both local and nonlocal MLE methods. Numerical and experimental analyses indicated the superior performance of this multispectral method for estimation of noise SD.

Improved determination of the myelin water fraction in human brain using magnetic resonance imaging through Bayesian analysis of mcDESPOT

Myelin water fraction (MWF) mapping with magnetic resonance imaging has led to the ability to directly observe myelination and demyelination in both the developing brain and in disease. Multicomponent driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) has been proposed as a rapid approach for multicomponent relaxometry and has been applied to map MWF in the human brain. However, even for the simplest two-pool signal model consisting of myelin-associated and non-myelin-associated water, the dimensionality of the parameter space for obtaining MWF estimates remains high. This renders parameter estimation difficult, especially at low-to-moderate signal-to-noise ratios (SNRs), due to the presence of local minima and the flatness of the fit residual energy surface used for parameter determination using conventional nonlinear least squares (NLLS)-based algorithms. In this study, we introduce three Bayesian approaches for analysis of the mcDESPOT signal model to determine MWF. Given the high-dimensional nature of the mcDESPOT signal model, and, therefore the high-dimensional marginalizations over nuisance parameters needed to derive the posterior probability distribution of the MWF, the Bayesian analyses introduced here use different approaches to reduce the dimensionality of the parameter space. The first approach uses normalization by average signal amplitude, and assumes that noise can be accurately estimated from signal-free regions of the image. The second approach likewise uses average amplitude normalization, but incorporates a full treatment of noise as an unknown variable through marginalization. The third approach does not use amplitude normalization and incorporates marginalization over both noise and signal amplitude. Through extensive Monte Carlo numerical simulations and analysis of in vivo human brain datasets exhibiting a range of SNR and spatial resolution, we demonstrated markedly improved accuracy and precision in the estimation of MWF using these Bayesian methods as compared to the stochastic region contraction (SRC) implementation of NLLS.

Spherical Deconvolution of Multichannel Diffusion MRI Data with Non-Gaussian Noise Models and Spatial Regularization

Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on many factors such as the number of coils and the methodology used to combine multichannel MRI signals. Indeed, the two prevailing methods for multichannel signal combination lead to noise patterns better described by Rician and noncentral Chi distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in human brain data.

A majorize-minimize framework for Rician and non-central chi MR images

The statistics of many MR magnitude images are described by the non-central chi (NCC) family of probability distributions, which includes the Rician distribution as a special case. These distributions have complicated negative log-likelihoods that are nontrivial to optimize. This paper describes a novel majorize-minimize framework for NCC data that allows penalized maximum likelihood estimates to be obtained by solving a series of much simpler regularized least-squares surrogate problems. The proposed framework is general and can be useful in a range of applications. We illustrate the potential advantages of the framework with real and simulated data in two contexts: 1) MR image denoising and 2) diffusion profile estimation in high angular resolution diffusion MRI. The proposed approach is shown to yield improved results compared to methods that model the noise statistics inaccurately and faster computation relative to commonly-used nonlinear optimization techniques.

Brain MR image denoising for Rician noise using pre-smooth non-local means filter

BACKGROUND

Magnetic resonance imaging (MRI) is corrupted by Rician noise, which is image dependent and computed from both real and imaginary images. Rician noise makes image-based quantitative measurement difficult. The non-local means (NLM) filter has been proven to be effective against additive noise.

METHODS

Considering the characteristics of both Rician noise and the NLM filter, this study proposes a frame for a pre-smoothing NLM (PSNLM) filter combined with image transformation. In the PSNLM frame, noisy MRI is first transformed into an image in which noise can be treated as additive noise. Second, the transformed MRI is pre-smoothed via a traditional denoising method. Third, the NLM filter is applied to the transformed MRI, with weights that are computed from the pre-smoothed image. Finally, inverse transformation is performed on the denoised MRI to obtain the denoising results.

RESULTS

To test the performance of the proposed method, both simulated and real patient data are used, and various pre-smoothing (Gaussian, median, and anisotropic filters) and image transformation [squared magnitude of the MRI, and forward and inverse variance-stabilizing trans-formations (VST)] methods are used to reduce noise. The performance of the proposed method is evaluated through visual inspection and quantitative comparison of the peak signal-to-noise ratio of the simulated data. The real data include Alzheimer's disease patients and normal controls. For the real patient data, the performance of the proposed method is evaluated by detecting atrophy regions in the hippocampus and the parahippocampal gyrus.

CONCLUSIONS

The comparison of the experimental results demonstrates that using a Gaussian pre-smoothing filter and VST produce the best results for the peak signal-to-noise ratio (PSNR) and atrophy detection.

Local estimation of the noise level in MRI using structural adaptation

We present a method for local estimation of the signal-dependent noise level in magnetic resonance images. The procedure uses a multi-scale approach to adaptively infer on local neighborhoods with similar data distribution. It exploits a maximum-likelihood estimator for the local noise level. The validity of the method was evaluated on repeated diffusion data of a phantom and simulated data using T1-data corrupted with artificial noise. Simulation results were compared with a recently proposed estimate. The method was also applied to a high-resolution diffusion dataset to obtain improved diffusion model estimation results and to demonstrate its usefulness in methods for enhancing diffusion data.

Data distributions in magnetic resonance images: a review

Many image processing methods applied to magnetic resonance (MR) images directly or indirectly rely on prior knowledge of the statistical data distribution that characterizes the MR data. Also, data distributions are key in many parameter estimation problems and strongly relate to the accuracy and precision with which parameters can be estimated. This review paper provides an overview of the various distributions that occur when dealing with MR data, considering both single-coil and multiple-coil acquisition systems. The paper also summarizes how knowledge of the MR data distributions can be used to construct optimal parameter estimators and answers the question as to what precision may be achieved ultimately from a particular MR image.

Noise estimation in parallel MRI: GRAPPA and SENSE

Parallel imaging methods allow to increase the acquisition rate via subsampled acquisitions of the k-space. SENSE and GRAPPA are the most popular reconstruction methods proposed in order to suppress the artifacts created by this subsampling. The reconstruction process carried out by both methods yields to a variance of noise value which is dependent on the position within the final image. Hence, the traditional noise estimation methods - based on a single noise level for the whole image - fail. In this paper we propose a novel methodology to estimate the spatial dependent pattern of the variance of noise in SENSE and GRAPPA reconstructed images. In both cases, some additional information must be known beforehand: the sensitivity maps of each receiver coil in the SENSE case and the reconstruction coefficients for GRAPPA.

Laplacian based non-local means denoising of MR images with Rician noise

Magnetic Resonance (MR) image is often corrupted with a complex white Gaussian noise (Rician noise) which is signal dependent. Considering the special characteristics of Rician noise, we carry out nonlocal means denoising on squared magnitude images and compensate the introduced bias. In this paper, we propose an algorithm which not only preserves the edges and fine structures but also performs efficient denoising. For this purpose we have used a Laplacian of Gaussian (LoG) filter in conjunction with a nonlocal means filter (NLM). Further, to enhance the edges and to accelerate the filtering process, only a few similar patches have been preselected on the basis of closeness in edge and inverted mean values. Experiments have been conducted on both simulated and clinical data sets. The qualitative and quantitative measures demonstrate the efficacy of the proposed method.

Anisotropic diffusion filtering for correlated multiple-coil MRI

Recently, some methods have been proposed for filtering multi-coil MRI acquisitions with correlation between coils. Those methods are based on statistical models of noise to develop a Linear Minimum Mean Square Error (LMMSE) filter. The advantage of LMMSE-based filters stems from their simplicity and robustness. However, they exhibit some drawbacks: their performance strongly depends on the underlying statistical model and on the way the local moments are estimated. The first problem can be avoided when considering effective values provided by recent studies on the models of noise in multi-coil systems with correlation between coils. However, the local moments are estimated in square neighborhoods which can include different kinds of tissues. Thus, the local variance is biased towards upper values, which results in an inaccurate estimate in regions close to tissue boundaries. In this work we propose to overcome this problem by introducing an anisotropic diffusion step in the LMMSE estimate for correlated multi-coil systems which improves the estimation of the signal in regions where other LMMSE methods fail. Results demonstrate the better behavior in different noisy scenarios.