Local estimation of the noise level in MRI using structural adaptation

Characterizing patterns of DTI variance in aging brains

Background

As large analyses merge data across sites, a deeper understanding of variance in statistical assessment across the sources of data becomes critical for valid analyses. Diffusion tensor imaging (DTI) exhibits spatially varying and correlated noise, so care must be taken with distributional assumptions.

Purpose

We characterize the role of physiology, subject compliance, and the interaction of subject with the scanner in the understanding of DTI variability, as modeled in spatial variance of derived metrics in homogeneous regions.

Methods

We analyze DTI data from 1035 subjects in the Baltimore Longitudinal Study of Aging (BLSA), with ages ranging from 22.4 to 103 years old. For each subject, up to 12 longitudinal sessions were conducted. We assess variance of DTI scalars within regions of interest (ROIs) defined by four segmentation methods and investigate the relationships between the variance and covariates, including baseline age, time from the baseline (referred to as "interval"), motion, sex, and whether it is the first scan or the second scan in the session.

Results

Covariate effects are heterogeneous and bilaterally symmetric across ROIs. Inter-session interval is positively related (p ≪ 0.001) to FA variance in the cuneus and occipital gyrus, but negatively (p ≪ 0.001) in the caudate nucleus. Males show significantly (p ≪ 0.001) higher FA variance in the right putamen, thalamus, body of the corpus callosum, and cingulate gyrus. In 62 out of 176 ROIs defined by the Eve type-1 atlas, an increase in motion is associated (p < 0.05) with a decrease in FA variance. Head motion increases during the rescan of DTI (Δμ = 0.045 millimeters per volume).

Conclusions

The effects of each covariate on DTI variance, and their relationships across ROIs are complex. Ultimately, we encourage researchers to include estimates of variance when sharing data and consider models of heteroscedasticity in analysis. This work provides a foundation for study planning to account for regional variations in metric variance.

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.

Spinal cord atrophy in a primary progressive multiple sclerosis trial: Improved sample size using GBSI

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The GBSI provided clinically meaningful measurements of spinal cord atrophy, with low sample size.

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Deriving spinal cord atrophy from brain MRI using the GBSI is easier than spinal cord MRI.

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Spinal cord atrophy on GBSI could be used as a secondary outcome measure.

Background

We aimed to evaluate the implications for clinical trial design of the generalised boundary-shift integral (GBSI) for spinal cord atrophy measurement.

Methods

We included 220 primary-progressive multiple sclerosis patients from a phase 2 clinical trial, with baseline and week-48 3DT1-weighted MRI of the brain and spinal cord (1 × 1 × 1 mm³), acquired separately. We obtained segmentation-based cross-sectional spinal cord area (CSA) at C1-2 (from both brain and spinal cord MRI) and C2-5 levels (from spinal cord MRI) using DeepSeg, and, then, we computed corresponding GBSI.

Results

Depending on the spinal cord segment, we included 67.4–98.1% patients for CSA measurements, and 66.9–84.2% for GBSI. Spinal cord atrophy measurements obtained with GBSI had lower measurement variability, than corresponding CSA. Looking at the image noise floor, the lowest median standard deviation of the MRI signal within the cerebrospinal fluid surrounding the spinal cord was found on brain MRI at the C1-2 level. Spinal cord atrophy derived from brain MRI was related to the corresponding measures from dedicated spinal cord MRI, more strongly for GBSI than CSA. Spinal cord atrophy measurements using GBSI, but not CSA, were associated with upper and lower limb motor progression.

Discussion

Notwithstanding the reduced measurement variability, the clinical correlates, and the possibility of using brain acquisitions, spinal cord atrophy using GBSI should remain a secondary outcome measure in MS studies, until further advancements increase the quality of acquisition and reliability of processing.

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.

MK-curve - Characterizing the relation between mean kurtosis and alterations in the diffusion MRI signal

Diffusion kurtosis imaging (DKI) is a diffusion MRI (dMRI) technique to quantify brain microstructural properties. While DKI measures are sensitive to tissue alterations, they are also affected by signal alterations caused by imaging artifacts such as noise, motion and Gibbs ringing. Consequently, DKI often yields output parameter values (e.g. mean kurtosis; MK) that are implausible. These include implausible values that are outside of the range dictated by physics/biology, and visually apparent implausible values that form unexpected discontinuities, being too high or too low comparing with their neighborhood. These implausible values will introduce bias into any following data analyses (e.g. between-population statistical computation). Existing studies have attempted to correct implausible DKI parameter values in multiple ways; however, these approaches are not always effective. In this study, we propose a novel method for detecting and correcting voxels with implausible values to enable improved DKI parameter estimation. In particular, we focus on MK parameter estimation. We first characterize the relation between MK and alterations in the dMRI signal including diffusion weighted images (DWIs) and the baseline (b0) images. This is done by calculating MK for a range of synthetic DWI or b0 for each voxel, and generating curves (MK-curve) representing how alterations to the input dMRI signals affect the resulting output MK. We find that voxels with implausible MK values are more likely caused by artifacts in the b0 images than artifacts in DWIs with higher b-values. Accordingly, two characteristic b0 values, which define a range of synthetic b0 values that generate implausible MK values, are identified on the MK-curve. Based on this characterization, we propose an automatic approach for detection of voxels with implausible MK values by comparing a voxel's original b0 signal to the identified two characteristic b0 values, along with a correction strategy to replace the original b0 in each detected implausible voxel with a synthetic b0 value computed from the MK-curve. We evaluate the method on a DKI phantom dataset and dMRI datasets from the Human Connectome Project (HCP), and we compare the proposed correction method with other previously proposed correction methods. Results show that our proposed method is able to identify and correct most voxels with implausible DKI parameter values as well as voxels with implausible diffusion tensor parameter values.

Local Indicators of Spatial Autocorrelation (LISA): Application to Blind Noise-Based Perceptual Quality Metric Index for Magnetic Resonance Images

Noise-based quality evaluation of MRI images is highly desired in noise-dominant environments. Current noise-based MRI quality evaluation methods have drawbacks which limit their effective performance. Traditional full-reference methods such as SNR and most of the model-based techniques cannot provide perceptual quality metrics required for accurate diagnosis, treatment and monitoring of diseases. Although techniques based on the Moran coefficients are perceptual quality metrics, they are full-reference methods and will be ineffective in applications where the reference image is not available. Furthermore, the predicted quality scores are difficult to interpret because their quality indices are not standardized. In this paper, we propose a new no-reference perceptual quality evaluation method for grayscale images such as MRI images. Our approach is formulated to mimic how humans perceive an image. It transforms noise level into a standardized perceptual quality score. Global Moran statistics is combined with local indicators of spatial autocorrelation in the form of local Moran statistics. Quality score is predicted from perceptually weighted combination of clustered and random pixels. Performance evaluation, comparative performance evaluation and validation by human observers, shows that the proposed method will be a useful tool in the evaluation of retrospectively acquired MRI images and the evaluation of noise reduction algorithms.

De-noising of 3D multiple-coil MR images using modified LMMSE estimator

De-noising is a crucial topic in Magnetic Resonance Imaging (MRI) which focuses on less loss of Magnetic Resonance (MR) image information and details preservation during the noise suppression. Nowadays multiple-coil MRI system is preferred to single one due to its acceleration in the imaging process. Due to the fact that the model of noise in single-coil and multiple-coil MRI systems are different, the de-noising methods that mostly are adapted to single-coil MRI systems, do not work appropriately with multiple-coil one. The model of noise in single-coil MRI systems is Rician while in multiple-coil one (if no subsampling occurs in k-space or GRAPPA reconstruction process is being done in the coils), it obeys noncentral Chi (nc-χ). In this paper, a new filtering method based on the Linear Minimum Mean Square Error (LMMSE) estimator is proposed for multiple-coil MR Images ruined by nc-χ noise. In the presented method, to have an optimum similarity selection of voxels, the Bayesian Mean Square Error (BMSE) criterion is used and proved for nc-χ noise model and also a nonlocal voxel selection methodology is proposed for nc-χ distribution. The results illustrate robust and accurate performance compared to the related state-of-the-art methods, either on ideal nc-χ images or GRAPPA reconstructed ones.

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.

Image denoising substantially improves accuracy and precision of intravoxel incoherent motion parameter estimates

Applicability of intravoxel incoherent motion (IVIM) imaging in the clinical setting is hampered by the limited reliability in particular of the perfusion-related parameter estimates. To alleviate this problem, various advanced postprocessing methods have been introduced. However, the underlying algorithms are not readily available and generally suffer from an increased computational burden. Contrary, several computationally fast image denoising methods have recently been proposed which are accessible online and may improve reliability of IVIM parameter estimates. The objective of the present work is to investigate the impact of image denoising on accuracy and precision of IVIM parameter estimates using comprehensive in-silico and in-vivo experiments. Image denoising is performed with four different algorithms that work on magnitude data: two algorithms which are based on nonlocal means (NLM) filtering, one algorithm that relies on local principal component analysis (LPCA) of the diffusion-weighted images, and another algorithms that exploits joint rank and edge constraints (JREC). Accuracy and precision of IVIM parameter estimates is investigated in an in-silico brain phantom and an in-vivo ground truth as a function of the signal-to-noise ratio for spatially homogenous and inhomogenous levels of Rician noise. Moreover, precision is evaluated using bootstrap analysis of in-vivo measurements. In the experiments, IVIM parameters are computed a) by using a segmented fit method and b) by performing a biexponential fit of the entire attenuation curve based on nonlinear least squares estimates. Irrespective of the fit method, the results demonstrate that reliability of IVIM parameter estimates is substantially improved by image denoising. The experiments show that the LPCA and the JREC algorithms perform in a similar manner and outperform the NLM-related methods. Relative to noisy data, accuracy of the IVIM parameters in the in-silico phantom improves after image denoising by 76–79%, 79–81%, 84–99% and precision by 74–80%, 80–83%, 84–95% for the perfusion fraction, the diffusion coefficient, and the pseudodiffusion coefficient, respectively, when the segmented fit method is used. Beyond that, the simulations reveal that denoising performance is not impeded by spatially inhomogeneous levels of Rician noise in the image. Since all investigated algorithms are freely available and work on magnitude data they can be readily applied in the clinical setting which may foster transition of IVIM imaging into clinical practice.

Diffusion MRI noise mapping using random matrix theory

PURPOSE

To estimate the spatially varying noise map using a redundant series of magnitude MR images.

METHODS

We exploit redundancy in non-Gaussian distributed multidirectional diffusion MRI data by identifying its noise-only principal components, based on the theory of noisy covariance matrices. The bulk of principal component analysis eigenvalues, arising due to noise, is described by the universal Marchenko-Pastur distribution, parameterized by the noise level. This allows us to estimate noise level in a local neighborhood based on the singular value decomposition of a matrix combining neighborhood voxels and diffusion directions.

RESULTS

We present a model-independent local noise mapping method capable of estimating the noise level down to about 1% error. In contrast to current state-of-the-art techniques, the resultant noise maps do not show artifactual anatomical features that often reflect physiological noise, the presence of sharp edges, or a lack of adequate a priori knowledge of the expected form of MR signal.

CONCLUSIONS

Simulations and experiments show that typical diffusion MRI data exhibit sufficient redundancy that enables accurate, precise, and robust estimation of the local noise level by interpreting the principal component analysis eigenspectrum in terms of the Marchenko-Pastur distribution. Magn Reson Med 76:1582-1593, 2016. © 2015 International Society for Magnetic Resonance in Medicine.