Spatially variant noise estimation in MRI: a homomorphic approach

Reduced cross-scanner variability using vendor-agnostic sequences for single-shell diffusion MRI

PURPOSE

To reduce the inter-scanner variability of diffusion MRI (dMRI) measures between scanners from different vendors by developing a vendor-neutral dMRI pulse sequence using the open-source vendor-agnostic Pulseq platform.

METHODS

We implemented a standard EPI based dMRI sequence in Pulseq. We tested it on two clinical scanners from different vendors (Siemens Prisma and GE Premier), systematically evaluating and comparing the within- and inter-scanner variability across the vendors, using both the vendor-provided and Pulseq dMRI sequences. Assessments covered both a diffusion phantom and three human subjects, using standard error (SE) and Lin's concordance correlation to measure the repeatability and reproducibility of standard DTI metrics including fractional anisotropy (FA) and mean diffusivity (MD).

RESULTS

Identical dMRI sequences were executed on both scanners using Pulseq. On the phantom, the Pulseq sequence showed more than a 2.5× reduction in SE (variability) across Siemens and GE scanners. Furthermore, Pulseq sequences exhibited markedly reduced SE in-vivo, maintaining scan-rescan repeatability while delivering lower variability in FA and MD (more than 50% reduction in cortical/subcortical regions) compared to vendor-provided sequences.

CONCLUSION

The Pulseq diffusion sequence reduces the cross-scanner variability for both phantom and in-vivo data, which will benefit multi-center neuroimaging studies and improve the reproducibility of neuroimaging studies.

Neural orientation distribution fields for estimation and uncertainty quantification in diffusion MRI

Inferring brain connectivity and structure in-vivo requires accurate estimation of the orientation distribution function (ODF), which encodes key local tissue properties. However, estimating the ODF from diffusion MRI (dMRI) signals is a challenging inverse problem due to obstacles such as significant noise, high-dimensional parameter spaces, and sparse angular measurements. In this paper, we address these challenges by proposing a novel deep-learning based methodology for continuous estimation and uncertainty quantification of the spatially varying ODF field. We use a neural field (NF) to parameterize a random series representation of the latent ODFs, implicitly modeling the often ignored but valuable spatial correlation structures in the data, and thereby improving efficiency in sparse and noisy regimes. An analytic approximation to the posterior predictive distribution is derived which can be used to quantify the uncertainty in the ODF estimate at any spatial location, avoiding the need for expensive resampling-based approaches that are typically employed for this purpose. We present empirical evaluations on both synthetic and real in-vivo diffusion data, demonstrating the advantages of our method over existing approaches.

A translational MRI approach to validate acute axonal damage detection as an early event in multiple sclerosis

Axonal degeneration is a central pathological feature of multiple sclerosis and is closely associated with irreversible clinical disability. Current noninvasive methods to detect axonal damage in vivo are limited in their specificity and clinical applicability, and by the lack of proper validation. We aimed to validate an MRI framework based on multicompartment modeling of the diffusion signal (AxCaliber) in rats in the presence of axonal pathology, achieved through injection of a neurotoxin damaging the neuronal terminal of axons. We then applied the same MRI protocol to map axonal integrity in the brain of multiple sclerosis relapsing-remitting patients and age-matched healthy controls. AxCaliber is sensitive to acute axonal damage in rats, as demonstrated by a significant increase in the mean axonal caliber along the targeted tract, which correlated with neurofilament staining. Electron microscopy confirmed that increased mean axonal diameter is associated with acute axonal pathology. In humans with multiple sclerosis, we uncovered a diffuse increase in mean axonal caliber in most areas of the normal-appearing white matter, preferentially affecting patients with short disease duration. Our results demonstrate that MRI-based axonal diameter mapping is a sensitive and specific imaging biomarker that links noninvasive imaging contrasts with the underlying biological substrate, uncovering generalized axonal damage in multiple sclerosis as an early event.

Quantitative MRI in Multiple Sclerosis: From Theory to Application

Quantitative MR imaging techniques allow evaluating different aspects of brain microstructure, providing meaningful information about the pathophysiology of damage in CNS disorders. In the study of patients with MS, quantitative MR imaging techniques represent an invaluable tool for studying changes in myelin and iron content occurring in the context of inflammatory and neurodegenerative processes. In the first section of this review, we summarize the physics behind quantitative MR imaging, here defined as relaxometry and quantitative susceptibility mapping, and describe the neurobiological correlates of quantitative MR imaging findings. In the second section, we focus on quantitative MR imaging application in MS, reporting the main findings in both the gray and white matter compartments, separately addressing macroscopically damaged and normal-appearing parenchyma.

Spatiotemporal encoding MRI using subspace-constrained sampling and locally-low-rank regularization: Applications to diffusion weighted and diffusion kurtosis imaging of human brain and prostate

The benefits of performing locally low-rank (LLR) reconstructions on subsampled diffusion weighted and diffusion kurtosis imaging data employing spatiotemporal encoding (SPEN) methods, is investigated. SPEN allows for self-referenced correction of motion-induced phase errors in case of interleaved diffusion-oriented acquisitions, and allows one to overcome distortions otherwise observed along EPI's phase-encoded dimension. In combination with LLR-based reconstructions of the pooled imaging data and with a joint subsampling of b-weighted and interleaved images, additional improvements in terms of sensitivity as well as shortened acquisition times are demonstrated, without noticeable penalties. Details on how the LLR-regularized, subspace-constrained image reconstructions were adapted to SPEN are given; the improvements introduced by adopting these reconstruction frameworks for the accelerated acquisition of diffusivity and of kurtosis imaging data in both relatively homogeneous regions like the human brain and in more challenging regions like the human prostate, are presented and discussed within the context of similar efforts in the field.

Fast, Accurate, and Robust T2 Mapping of Articular Cartilage by Neural Networks

For T2 mapping, the underlying mono-exponential signal decay is traditionally quantified by non-linear Least-Squares Estimation (LSE) curve fitting, which is prone to outliers and computationally expensive. This study aimed to validate a fully connected neural network (NN) to estimate T2 relaxation times and to assess its performance versus LSE fitting methods. To this end, the NN was trained and tested in silico on a synthetic dataset of 75 million signal decays. Its quantification error was comparatively evaluated against three LSE methods, i.e., traditional methods without any modification, with an offset, and one with noise correction. Following in-situ acquisition of T2 maps in seven human cadaveric knee joint specimens at high and low signal-to-noise ratios, the NN and LSE methods were used to estimate the T2 relaxation times of the manually segmented patellofemoral cartilage. In-silico modeling at low signal-to-noise ratio indicated significantly lower quantification error for the NN (by medians of 6−33%) than for the LSE methods (p < 0.001). These results were confirmed by the in-situ measurements (medians of 10−35%). T2 quantification by the NN took only 4 s, which was faster than the LSE methods (28−43 s). In conclusion, NNs provide fast, accurate, and robust quantification of T2 relaxation times.

Artifact- and content-specific quality assessment for MRI with image rulers

In clinical practice MR images are often first seen by radiologists long after the scan. If image quality is inadequate either patients have to return for an additional scan, or a suboptimal interpretation is rendered. An automatic image quality assessment (IQA) would enable real-time remediation. Existing IQA works for MRI give only a general quality score, agnostic to the cause of and solution to low-quality scans. Furthermore, radiologists' image quality requirements vary with the scan type and diagnostic task. Therefore, the same score may have different implications for different scans. We propose a framework with multi-task CNN model trained with calibrated labels and inferenced with image rulers. Labels calibrated by human inputs follow a well-defined and efficient labeling task. Image rulers address varying quality standards and provide a concrete way of interpreting raw scores from the CNN. The model supports assessments of two of the most common artifacts in MRI: noise and motion. It achieves accuracies of around 90%, 6% better than the best previous method examined, and 3% better than human experts on noise assessment. Our experiments show that label calibration, image rulers, and multi-task training improve the model's performance and generalizability.

SNR-enhanced diffusion MRI with structure-preserving low-rank denoising in reproducing kernel Hilbert spaces

PURPOSE

To introduce, develop, and evaluate a novel denoising technique for diffusion MRI that leverages nonlinear redundancy in the data to boost the SNR while preserving signal information.

METHODS

We exploit nonlinear redundancy of the dMRI data by means of kernel principal component analysis (KPCA), a nonlinear generalization of PCA to reproducing kernel Hilbert spaces. By mapping the signal to a high-dimensional space, a higher level of redundant information is exploited, thereby enabling better denoising than linear PCA. We implement KPCA with a Gaussian kernel, with parameters automatically selected from knowledge of the noise statistics, and validate it on realistic Monte Carlo simulations as well as with in vivo human brain submillimeter and low-resolution dMRI data. We also demonstrate KPCA denoising on multi-coil dMRI data.

RESULTS

SNR improvements up to 2.7 × were obtained in real in vivo datasets denoised with KPCA, in comparison to SNR gains of up to 1.8 × using a linear PCA denoising technique called Marchenko-Pastur PCA (MPPCA). Compared to gold-standard dataset references created from averaged data, we showed that lower normalized root mean squared error was achieved with KPCA compared to MPPCA. Statistical analysis of residuals shows that anatomical information is preserved and only noise is removed. Improvements in the estimation of diffusion model parameters such as fractional anisotropy, mean diffusivity, and fiber orientation distribution functions were also demonstrated.

CONCLUSION

Nonlinear redundancy of the dMRI signal can be exploited with KPCA, which allows superior noise reduction/SNR improvements than the MPPCA method, without loss of signal information.

Digital Image Noise Estimation Using DWT Coefficients

Noise type and strength estimation are important in many image processing applications like denoising, compression, video tracking, etc. There are many existing methods for estimation of the type of noise and its strength in digital images. These methods mostly rely on the transform or spatial domain information of images. We propose a hybrid Discrete Wavelet Transform (DWT) and edge information removal based algorithm to estimate the strength of Gaussian noise in digital images. The wavelet coefficients corresponding to spatial domain edges are excluded from noise estimate calculation using a Sobel edge detector. The accuracy of the proposed algorithm is further increased using polynomial regression. Parseval's theorem mathematically validates the proposed algorithm. The performance of the proposed algorithm is evaluated on a standard LIVE image dataset. Benchmarking results show that the proposed algorithm outperforms all other state of the art algorithms by a large margin over a wide range of noise.

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.

Simultaneous imaging of hard and soft biological tissues in a low-field dental MRI scanner

Magnetic Resonance Imaging (MRI) of hard biological tissues is challenging due to the fleeting lifetime and low strength of their response to resonant stimuli, especially at low magnetic fields. Consequently, the impact of MRI on some medical applications, such as dentistry, continues to be limited. Here, we present three-dimensional reconstructions of ex-vivo human teeth, as well as a rabbit head and part of a cow femur, all obtained at a field strength of 260 mT. These images are the first featuring soft and hard tissues simultaneously at sub-Tesla fields, and they have been acquired in a home-made, special-purpose, pre-medical MRI scanner designed with the goal of demonstrating dental imaging at low field settings. We encode spatial information with two pulse sequences: Pointwise-Encoding Time reduction with Radial Acquisition and a new sequence we have called Double Radial Non-Stop Spin Echo, which we find to perform better than the former. For image reconstruction we employ Algebraic Reconstruction Techniques (ART) as well as standard Fourier methods. An analysis of the resulting images shows that ART reconstructions exhibit a higher signal-to-noise ratio with a more homogeneous noise distribution.

The costs and benefits of estimating T1 of tissue alongside cerebral blood flow and arterial transit time in pseudo-continuous arterial spin labeling

Multi-post-labeling-delay pseudo-continuous arterial spin labeling (multi-PLD PCASL) allows for absolute quantification of the cerebral blood flow (CBF) as well as the arterial transit time (ATT). Estimating these perfusion parameters from multi-PLD PCASL data is a non-linear inverse problem, which is commonly tackled by fitting the single-compartment model (SCM) for PCASL, with CBF and ATT as free parameters. The longitudinal relaxation time of tissue T_1t is an important parameter in this model, as it governs the decay of the perfusion signal entirely upon entry in the imaging voxel. Conventionally, T_1t is fixed to a population average. This approach can cause CBF quantification errors, as T_1t can vary significantly inter- and intra-subject. This study compares the impact on CBF quantification, in terms of accuracy and precision, of either fixing T_1t , the conventional approach, or estimating it alongside CBF and ATT. It is shown that the conventional approach can cause a significant bias in CBF. Indeed, simulation experiments reveal that if T_1t is fixed to a value that is 10% off its true value, this may already result in a bias of 15% in CBF. On the other hand, as is shown by both simulation and real data experiments, estimating T_1t along with CBF and ATT results in a loss of CBF precision of the same order, even if the experiment design is optimized for the latter estimation problem. Simulation experiments suggest that an optimal balance between accuracy and precision of CBF estimation from multi-PLD PCASL data can be expected when using the two-parameter estimator with a fixed T_1t value between population averages of T_1t and the longitudinal relaxation time of blood T_1b .

Supporting measurements or more averages? How to quantify cerebral blood flow most reliably in 5 minutes by arterial spin labeling

Purpose

To determine whether sacrificing part of the scan time of pseudo‐continuous arterial spin labeling (PCASL) for measurement of the labeling efficiency and blood T1 is beneficial in terms of CBF quantification reliability.

Methods

In a simulation framework, 5‐minute scan protocols with different scan time divisions between PCASL data acquisition and supporting measurements were evaluated in terms of CBF estimation variability across both noise and ground truth parameter realizations taken from the general population distribution. The entire simulation experiment was repeated for a single‐post‐labeling delay (PLD), multi‐PLD, and free‐lunch time‐encoded (te‐FL) PCASL acquisition strategy. Furthermore, a real data study was designed for preliminary validation.

Results

For the considered population statistics, measuring the labeling efficiency and the blood T1 proved beneficial in terms of CBF estimation variability for any distribution of the 5‐minute scan time compared to only acquiring ASL data. Compared to single‐PLD PCASL without support measurements as recommended in the consensus statement, a 26%, 33%, and 42% reduction in relative CBF estimation variability was found for optimal combinations of supporting measurements with single‐PLD, free‐lunch, and multi‐PLD PCASL data acquisition, respectively. The benefit of taking the individual variation of blood T1 into account was also demonstrated in the real data experiment.

Conclusions

Spending time to measure the labeling efficiency and the blood T1 instead of acquiring more averages of the PCASL data proves to be advisable for robust CBF quantification in the general population.

Non-Local SVD Denoising of MRI Based on Sparse Representations

Magnetic Resonance (MR) Imaging is a diagnostic technique that produces noisy images, which must be filtered before processing to prevent diagnostic errors. However, filtering the noise while keeping fine details is a difficult task. This paper presents a method, based on sparse representations and singular value decomposition (SVD), for non-locally denoising MR images. The proposed method prevents blurring, artifacts, and residual noise. Our method is composed of three stages. The first stage divides the image into sub-volumes, to obtain its sparse representation, by using the KSVD algorithm. Then, the global influence of the dictionary atoms is computed to upgrade the dictionary and obtain a better reconstruction of the sub-volumes. In the second stage, based on the sparse representation, the noise-free sub-volume is estimated using a non-local approach and SVD. The noise-free voxel is reconstructed by aggregating the overlapped voxels according to the rarity of the sub-volumes it belongs, which is computed from the global influence of the atoms. The third stage repeats the process using a different sub-volume size for producing a new filtered image, which is averaged with the previously filtered images. The results provided show that our method outperforms several state-of-the-art methods in both simulated and real data.

Stimulated-echo diffusion-weighted imaging with moderate b values for the detection of prostate cancer

OBJECTIVES

Conventional spin-echo (SE) DWI leads to a fundamental trade-off depending on the b value: high b value provides better lesion contrast-to-noise ratio (CNR) by sacrificing signal-to-noise ratio (SNR), image quality, and quantitative reliability. A stimulated-echo (STE) DWI acquisition is evaluated for high-CNR imaging of prostate cancer while maintaining SNR and reliable apparent diffusion coefficient (ADC) mapping.

METHODS

In this prospective, IRB-approved study, 27 patients with suspected prostate cancer (PCa) were scanned with three DWI sequences (SE b = 800 s/mm², SE b = 1500 s/mm², and STE b = 800 s/mm²) after informed consent was obtained. ROIs were drawn on biopsy-confirmed cancer and non-cancerous tissue to perform quantitative SNR, CNR, and ADC measurements. Qualitative metrics (SNR, CNR, and overall image quality) were evaluated by three experienced radiologists. Metrics were compared pairwise between the three acquisitions using a t test (quantitative metrics) and Wilcoxon rank test (qualitative metrics).

RESULTS

Quantitative measurements showed that STE DWI at b = 800 s/mm² has significantly better SNR compared to SE DWI at b = 1500 s/mm² (p < 0.0001) and comparable CNR to high-b value SE DWI at b = 1500 s/mm² (p < 0.05) in the peripheral zone. Qualitative assessment showed preference to STE b = 800 s/mm² in SNR and SE b = 1500 s/mm² in CNR. The overall image quality and lesion detectability among most readers showed no significant preference between STE b = 800 s/mm² and SE b = 1500 s/mm². Further, STE DWI had similar ADC contrast between lesion and normal tissue as SE DWI at b = 800 s/mm² (p = 0.90).

CONCLUSION

STE DWI has the potential to provide high-SNR, high-CNR imaging of prostate cancer while also enabling reliable ADC mapping.

KEY POINTS

• Quantitative analysis showed that STE DWI at b = 800 s/mm²is able to achieve simultaneously high CNR, high SNR, and reliable ADC mapping, compared to SE b = 800 s/mm²and SE b = 1500 s/mm². • Qualitative assessment by three readers showed that STE DWI at b = 800 s/mm²has significantly higher SNR than SE b = 1500 s/mm². No preference between SE b = 1500 s/mm²and STE b = 800 s/mm²was determined in terms of CNR with no missed lesions were found in both acquisitions. • A single STE DWI acquisition at moderate b value (800-1000 s/mm²) may provide sufficient image quality and quantitative reliability for prostate cancer imaging within a shorter scan time, in place of two DWI acquisitions (one with moderate b value and one with high b value).

Denoising of Diffusion MRI Data via Graph Framelet Matching in x-q Space

Diffusion magnetic resonance imaging (DMRI) suffers from lower signal-to-noise-ratio (SNR) due to MR signal attenuation associated with the motion of water molecules. To improve SNR, the non-local means (NLM) algorithm has demonstrated state-of-the-art performance in noise reduction. However, existing NLM algorithms do not take into account explicitly the fact that DMRI signal can vary significantly with local fiber orientations. Applying NLM naïvely can hence blur subtle structures and aggravate partial volume effects. To overcome this limitation, we improve NLM by performing neighborhood matching in non-flat domains and removing noise with information from both x -space (spatial domain) and q -space (wavevector domain). Specifically, we first encode the q -space sampling domain using a graph. We then perform graph framelet transforms to extract robust rotation-invariant features for each sampling point in x-q space. The resulting features are employed for robust neighborhood matching to locate recurrent information. Finally, we remove noise via an NLM framework. To adapt to the various types of noise in multi-coil MR imaging, we transform the signal before denoising so that it is Gaussian-distributed, allowing noise removal to be carried out in an unbiased manner. Our method is able to more effectively locate recurrent information in white matter structures with different orientations, avoiding the blurring effects caused by naïvely applying NLM. Experiments on synthetic, repetitively-acquired, and infant DMRI data demonstrate that our method is able to preserve subtle structures while effectively removing noise.

Segmentation-Based Blood Flow Parameter Refinement in Cerebrovascular Structures Using 4-D Arterial Spin Labeling MRA

OBJECTIVE

Cerebrovascular diseases are one of the main global causes of death and disability in the adult population. The preferred imaging modality for the diagnostic routine is digital subtraction angiography, an invasive modality. Time-resolved three-dimensional arterial spin labeling magnetic resonance angiography (4D ASL MRA) is an alternative non-invasive modality, which captures morphological and blood flow data of the cerebrovascular system, with high spatial and temporal resolution. This work proposes advanced medical image processing methods that extract the anatomical and hemodynamic information contained in 4D ASL MRA datasets.

METHODS

A previously published segmentation method, which uses blood flow data to improve its accuracy, is extended to estimate blood flow parameters by fitting a mathematical model to the measured vascular signal. The estimated values are then refined using regression techniques within the cerebrovascular segmentation. The proposed method was evaluated using fifteen 4D ASL MRA phantoms, with ground-truth morphological and hemodynamic data, fifteen 4D ASL MRA datasets acquired from healthy volunteers, and two 4D ASL MRA datasets from patients with a stenosis.

RESULTS

The proposed method reached an average Dice similarity coefficient of 0.957 and 0.938 in the phantom and real dataset segmentation evaluations, respectively. The estimated blood flow parameter values are more similar to the ground-truth values after the refinement step, when using phantoms. A qualitative analysis showed that the refined blood flow estimation is more realistic compared to the raw hemodynamic parameters.

CONCLUSION

The proposed method can provide accurate segmentations and blood flow parameter estimations in the cerebrovascular system using 4D ASL MRA datasets.

SIGNIFICANCE

The information obtained with the proposed method can help clinicians and researchers to study the cerebrovascular system non-invasively.

Application of Artificial Neural Network for Image Noise Level Estimation in the SVD domain

The blind additive white Gaussian noise level estimation is an important and a challenging area of digital image processing with numerous applications including image denoising and image segmentation. In this paper, a novel block-based noise level estimation algorithm is proposed. The algorithm relies on the artificial neural network to perform a complex image patch analysis in the singular value decomposition (SVD) domain and to evaluate noise level estimates. The algorithm exhibits the capacity to adjust the effective singular value tail length with respect to the observed noise levels. The results of comparative analysis show that the proposed ANN-based algorithm outperforms the alternative single stage block-based noise level estimating algorithm in the SVD domain in terms of mean square error (MSE) and average error for all considered choices of block size. The most significant improvements in MSE levels are obtained at low noise levels. For some test images, such as “Car” and “Girlface”, at σ = 1 , these improvements can be as high as 99% and 98.5%, respectively. In addition, the proposed algorithm eliminates the error-prone manual parameter fine-tuning and automates the entire noise level estimation process.

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.

Optimized Diffusion-Weighting Gradient Waveform Design (ODGD) formulation for motion compensation and concomitant gradient nulling

PURPOSE

To present a novel Optimized Diffusion-weighting Gradient waveform Design (ODGD) method for the design of minimum echo time (TE), bulk motion-compensated, and concomitant gradient (CG)-nulling waveforms for diffusion MRI.

METHODS

ODGD motion-compensated waveforms were designed for various moment-nullings M_n (n = 0, 1, 2), for a range of b-values, and spatial resolutions, both without (ODGD-M_n ) and with CG-nulling (ODGD-M_n -CG). Phantom and in-vivo (brain and liver) experiments were conducted with various ODGD waveforms to compare motion robustness, signal-to-noise ratio (SNR), and apparent diffusion coefficient (ADC) maps with state-of-the-art waveforms.

RESULTS

ODGD-M_n and ODGD-M_n -CG waveforms reduced the TE of state-of-the-art waveforms. This TE reduction resulted in significantly higher SNR (P < 0.05) in both phantom and in-vivo experiments. ODGD-M₁ improved the SNR of BIPOLAR (42.8 ± 5.3 vs. 32.9 ± 3.3) in the brain, and ODGD-M₂ the SNR of motion-compensated (MOCO) and Convex Optimized Diffusion Encoding-M₂ (CODE-M₂ ) (12.3 ± 3.6 vs. 9.7 ± 2.9 and 10.2 ± 3.4, respectively) in the liver. Further, ODGD-M₂ also showed excellent motion robustness in the liver. ODGD-M_n -CG waveforms reduced the CG-related dephasing effects of non CG-nulling waveforms in phantom and in-vivo experiments, resulting in accurate ADC maps.

CONCLUSIONS

ODGD waveforms enable motion-robust diffusion MRI with reduced TEs, increased SNR, and reduced ADC bias compared to state-of-the-art waveforms in theoretical results, simulations, phantoms and in-vivo experiments.

NOVIFAST: A Fast Algorithm for Accurate and Precise VFA MRI Mapping

In quantitative magnetic resonance mapping, the variable flip angle (VFA) steady state spoiled gradient recalled echo (SPGR) imaging technique is popular as it provides a series of high resolution weighted images in a clinically feasible time. Fast, linear methods that estimate maps from these weighted images have been proposed, such as DESPOT1 and iterative re-weighted linear least squares. More accurate, non-linear least squares (NLLS) estimators are in play, but these are generally much slower and require careful initialization. In this paper, we present NOVIFAST, a novel NLLS-based algorithm specifically tailored to VFA SPGR mapping. By exploiting the particular structure of the SPGR model, a computationally efficient, yet accurate and precise map estimator is derived. Simulation and in vivo human brain experiments demonstrate a twenty-fold speed gain of NOVIFAST compared with conventional gradient-based NLLS estimators while maintaining a high precision and accuracy. Moreover, NOVIFAST is eight times faster than the efficient implementations of the variable projection (VARPRO) method. Furthermore, NOVIFAST is shown to be robust against initialization.

Technical Note: Retrospective reduction in systematic differences across scanner changes by accounting for noise floor effects in diffusion tensor imaging

PURPOSE

The purpose of this study was to determine if retrospective correction for noise floor effects can reduce systematic differences and improve reproducibility across major scanner changes. Changes in scanner configuration can negatively impact quantitative MRI studies by introducing systematic differences between measurements that are due to the instrument, not biology. Noise floor rectification is a potential source of systematic differences in diffusion tensor imaging (DTI).

METHODS

Healthy volunteers were scanned before and after a major scanner change at four sites. DTI-based measures of tissue microstructure were calculated using a standard approach that ignores noise floor effects and using a maximum likelihood estimation (MLE) approach that accounts for the noise floor. Voxelwise estimates of systematic differences and reproducibility were evaluated.

RESULTS

Accounting for noise floor effects can reduce the extent of systematic differences and can improve reproducibility. However, when signal levels are high, accounting for the noise floor can have a deleterious effect. An empirical metric constructed to reflect the magnitude of noise floor effects signal-to-noise-floor ratio (SNFR). The MLE approach improves reproducibility for SNFR < 3.

CONCLUSIONS

Accounting for noise floor effects can boost the robustness of DTI measurements in the presence of scanner changes, potentially improving the reliability of DTI for studies of neurological disease.

A Bayesian Multiresolution Approach for Noise Removal in Medical Magnetic Resonance Images

A Bayesian approach using wavelet coefficient modeling is proposed for de-noising additive white Gaussian noise in medical magnetic resonance imaging (MRI). In a parallel acquisition process, the magnetic resonance image is affected by white Gaussian noise, which is additive in nature. A normal inverse Gaussian probability distribution function is taken for modeling the wavelet coefficients. A Bayesian approach is implemented for filtering the noisy wavelet coefficients. The maximum likelihood estimator and median absolute deviation estimator are used to find the signal parameters, signal variances, and noise variances of the distribution. The minimum mean square error estimator is used for estimating the true wavelet coefficients. The proposed method is simulated on MRI. Performance and image quality parameters show that the proposed method has the capability to reduce the noise more effectively than other state-of-the-art methods. The proposed method provides 8.83%, 2.02%, 6.61%, and 30.74% improvement in peak signal-to-noise ratio, structure similarity index, Pratt’s figure of merit, and Bhattacharyya coefficient, respectively, over existing well-accepted methods. The effectiveness of the proposed method is evaluated by using the mean squared difference (MSD) parameter. MSD shows the degree of dissimilarity and is 0.000324 for the proposed method, which is less than that of the other existing methods and proves the effectiveness of the proposed method. Experimental results show that the proposed method is capable of achieving better signal-to-noise ratio performance than other tested de-noising methods.

Autocalibration method for non-stationary CT bias correction

Computed tomography (CT) is a widely used imaging modality for screening and diagnosis. However, the deleterious effects of radiation exposure inherent in CT imaging require the development of image reconstruction methods which can reduce exposure levels. The development of iterative reconstruction techniques is now enabling the acquisition of low-dose CT images whose quality is comparable to that of CT images acquired with much higher radiation dosages. However, the characterization and calibration of the CT signal due to changes in dosage and reconstruction approaches is crucial to provide clinically relevant data. Although CT scanners are calibrated as part of the imaging workflow, the calibration is limited to select global reference values and does not consider other inherent factors of the acquisition that depend on the subject scanned (e.g. photon starvation, partial volume effect, beam hardening) and result in a non-stationary noise response. In this work, we analyze the effect of reconstruction biases caused by non-stationary noise and propose an autocalibration methodology to compensate it. Our contributions are: 1) the derivation of a functional relationship between observed bias and non-stationary noise, 2) a robust and accurate method to estimate the local variance, 3) an autocalibration methodology that does not necessarily rely on a calibration phantom, attenuates the bias caused by noise and removes the systematic bias observed in devices from different vendors. The validation of the proposed methodology was performed with a physical phantom and clinical CT scans acquired with different configurations (kernels, doses, algorithms including iterative reconstruction). The results confirmed the suitability of the proposed methods for removing the intra-device and inter-device reconstruction biases.

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.

Statistical characterization of noise for spatial standardization of CT scans: Enabling comparison with multiple kernels and doses

Computerized tomography (CT) is a widely adopted modality for analyzing directly or indirectly functional, biological and morphological processes by means of the image characteristics. However, the potential utilization of the information obtained from CT images is often limited when considering the analysis of quantitative information involving different devices, acquisition protocols or reconstruction algorithms. Although CT scanners are calibrated as a part of the imaging workflow, the calibration is circumscribed to global reference values and does not circumvent problems that are inherent to the imaging modality. One of them is the lack of noise stationarity, which makes quantitative biomarkers extracted from the images less robust and stable. Some methodologies have been proposed for the assessment of non-stationary noise in reconstructed CT scans. However, those methods focused on the non-stationarity only due to the reconstruction geometry and are mainly based on the propagation of the variance of noise throughout the whole reconstruction process. Additionally, the philosophy followed in the state-of-the-art methods is based on the reduction of noise, but not in the standardization of it. This means that, even if the noise is reduced, the statistics of the signal remain non-stationary, which is insufficient to enable comparisons between different acquisitions with different statistical characteristics. In this work, we propose a statistical characterization of noise in reconstructed CT scans that leads to a versatile statistical model that effectively characterizes different doses, reconstruction kernels, and devices. The statistical model is generalized to deal with the partial volume effect via a localized mixture model that also describes the non-stationarity of noise. Finally, we propose a stabilization scheme to achieve stationary variance. The validation of the proposed methodology was performed with a physical phantom and clinical CT scans acquired with different configurations (kernels, doses, algorithms including iterative reconstruction). The results confirmed its suitability to enable comparisons with different doses, and acquisition protocols.

A Unified Maximum Likelihood Framework for Simultaneous Motion and $T_{1}$ Estimation in Quantitative MR $T_{1}$ Mapping

In quantitative MR T₁ mapping, the spin-lattice relaxation time T₁ of tissues is estimated from a series of T₁ -weighted images. As the T₁ estimation is a voxel-wise estimation procedure, correct spatial alignment of the T₁ -weighted images is crucial. Conventionally, the T₁ -weighted images are first registered based on a general-purpose registration metric, after which the T₁ map is estimated. However, as demonstrated in this paper, such a two-step approach leads to a bias in the final T₁ map. In our work, instead of considering motion correction as a preprocessing step, we recover the motion-free T₁ map using a unified estimation approach. In particular, we propose a unified framework where the motion parameters and the T₁ map are simultaneously estimated with a Maximum Likelihood (ML) estimator. With our framework, the relaxation model, the motion model as well as the data statistics are jointly incorporated to provide substantially more accurate motion and T₁ parameter estimates. Experiments with realistic Monte Carlo simulations show that the proposed unified ML framework outperforms the conventional two-step approach as well as state-of-the-art model-based approaches, in terms of both motion and T₁ map accuracy and mean-square error. Furthermore, the proposed method was additionally validated in a controlled experiment with real T₁ -weighted data and with two in vivo human brain T₁ -weighted data sets, showing its applicability in real-life scenarios.

Knee imaging: Rapid three-dimensional fast spin-echo using compressed sensing

PURPOSE

To investigate the feasibility of using compressed sensing (CS) to accelerate three-dimensional fast spin-echo (3D-FSE) imaging of the knee.

MATERIALS AND METHODS

A 3D-FSE sequence was performed at 3T with CS (CUBE-CS with 3:16-minute scan time) and without CS (CUBE with 4:44-minute scan time) twice on the knees of 10 healthy volunteers to assess signal-to-noise ratio (SNR) using the addition-subtraction method and once on the knees of 50 symptomatic patients to assess diagnostic performance. SNR of cartilage, muscle, synovial fluid, and bone marrow on CUBE and CUBE-CS images were measured in the 10 healthy volunteers. The CUBE and CUBE-CS sequences of all 50 symptomatic patients were independently reviewed twice by two musculoskeletal radiologists. The radiologists used CUBE and CUBE-CS during each individual review to determine the presence or absence of knee joint pathology. Student's t-tests were used to compare SNR values between sequences, while the kappa statistic was used to determine agreement between sequences for detecting knee joint pathology. Sensitivity and specificity of CUBE and CUBE-CS for detecting knee joint pathology was also calculated in the 18 symptomatic patients who underwent subsequent arthroscopic knee surgery.

RESULTS

CUBE and CUBE-CS had similar SNR (P = 0.15-0.67) of cartilage, muscle, synovial fluid, and bone marrow. There was near-perfect to perfect agreement between CUBE and CUBE-CS for both radiologists for detecting cartilage and bone marrow edema lesions, medial and lateral meniscus tears, anterior cruciate ligament tears, effusions, and intra-articular bodies. CUBE and CUBE-CS had similar sensitivity (75.0-100%) and specificity (87.5-100%) for detecting 60 cartilage lesions, 20 meniscus tears, four anterior cruciate ligament tears, and four intra-articular bodies confirmed at surgery.

CONCLUSION

CS provided a 30% reduction in scan time for 3D-FSE imaging of the knee without a corresponding decrease in SNR or diagnostic performance.

LEVEL OF EVIDENCE

1 J. MAGN. RESON. IMAGING 2017;45:1712-1722.

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.

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.