Automatic estimation of the noise variance from the histogram of a magnetic resonance image

Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data

We propose a new goodness-of-fit test for the Rayleigh distribution which is based on a distributional fixed-point property of the Stein characterization. The limiting null distribution of the test is derived and the consistency against fixed alternatives is also shown. The results of a finite-sample comparison is presented, where we compare the power performance of the new test to a variety of other tests. In addition to existing tests for the Rayleigh distribution we also exploit the link between the exponential and Rayleigh distributions. This allows us to include some powerful tests developed specifically for the exponential distribution in the comparison. It is found that the new test outperforms competing tests for many of the alternative distributions. Interestingly, the highest estimated power, against all alternative distributions considered, is obtained by one of the tests specifically developed for the Rayleigh distribution and not by any of the exponentiality tests based on the transformed data. The use of the new test is illustrated on a real-world COVID-19 data set.

Opportunistic Use of Lumbar Magnetic Resonance Imaging for Osteoporosis Screening

Magnetic resonance imaging (MRI) is a routine assessment before spine surgery. We found that the opportunistic use of MRI with the vertebral bone quality (VBQ) score has good diagnostic ability, with a threshold value of VBQ > 3.0, in recognizing patients who may need further osteoporosis evaluation.

INTRODUCTION

The purpose of this study was to determine whether the opportunistic use of magnetic resonance imaging (MRI) is useful for identifying spine surgical patients who need further osteoporosis evaluation.

METHODS

This retrospective study evaluated 83 thoracolumbar spine surgery patients age ≥ 50 who received T1-weighted MRI. Opportunistic MRI was evaluated with the vertebral bone quality (VBQ) score, VBQ (fat) score, and signal-to-noise ratio (SNR). Each uses the median L1-L4 vertebral body signal intensities (SI) divided by either the L3 cerebrospinal fluid (CSF) SI, average SI of the L1 and S1 dorsal fat, or standard deviation (SD) of the background SI dorsal to the skin. Single-level VBQ was calculated as the ratio of the L1 vertebral body and L1 CSF SIs. Receiver-operator curve analysis was performed to determine diagnostic ability.

RESULTS

The mean age was 70.10, 80% were female, and 96% were Caucasian. The mean ± SD VBQ, single-level VBQ, VBQ (fat), and SNR were 3.39 ± 0.68, 3.56 ± 0.81, 3.95 ± 1.89, and 113.18 ± 77.26, respectively. Using area under the curve, the diagnostic ability of VBQ, single-level VBQ, VBQ (fat), and SNR for clinical osteoporosis were 0.806, 0.779, 0.608, and 0.586, respectively. Diagnostic threshold values identified with optimal sensitivity and specificity were VBQ of 2.95 and single-level VBQ of 3.06.

CONCLUSION

Opportunistic use of MRI is a simple, effective tool that may help recognize patients who are at risk for complications related to bone disease. A VBQ > 3.0 can identify patients who need additional diagnostic evaluation.

Rician Denoising Based on Correlated Local Features LMMSE Approach

In this study we propose a novel correction scheme that filters Magnetic Resonance Images data, by using a modified Linear Minimum Mean Square Error (LMMSE) estimator which takes into account the joint information of the local features. A closed-form analytical solution for our estimator is presented and it proves to make the filtering process far simpler and faster than other estimation techniques that rely on iterative optimization scheme and require multiple data samples. An experimental validation of our correction scheme was carried out through large scale experiments using both clinical and synthetic MR images, artificially corrupted with rician noise of σ varying from 1 to 40. These noisy images were filtered using our proposed method against the classical LMMSE, the Non-Local Means filter and the Nonlocality-Reinforced Convolutional Neural Networks (NRCNN) techniques. The results show an outstanding performance of our proposed method, given the fact that from σ ≈ 12 onwards, the proposed method outperforms all other methods. Another attention-grabbing feature of our method is that its Structural Similarity does not vary sharply [0.87, 0.95] across the σ spectrum as the other three techniques, which implies that this method can work on a wider range of deteriorated images than the rest of the techniques.

A Survey on State-of-the-art Denoising Techniques for Brain Magnetic Resonance Images

The accuracy of the magnetic resonance (MR) image diagnosis depends on the quality of the image, which degrades mainly due to noise and artifacts. The noise is introduced because of erroneous imaging environment or distortion in the transmission system. Therefore, denoising methods play an important role in enhancing the image quality. However, a tradeoff between denoising and preserving the structural details is required. Most of the existing surveys are conducted on a specific MR image modality or on limited denoising schemes. In this context, a comprehensive review on different MR image denoising techniques is inevitable. This survey suggests a new direction in categorizing the MR image denoising techniques. The categorization of the different image models used in medical image processing serves as the basis of our classification. This study includes recent improvements on deep learning-based denoising methods alongwith important traditional MR image denoising methods. The major challenges and their scope of improvement are also discussed. Further, many more evaluation indices are considered for a fair comparison. An elaborate discussion on selecting appropriate method and evaluation metric as per the kind of data is presented. This study may encourage researchers for further work in this domain.

Processing Pipeline for Atlas-Based Imaging Data Analysis of Structural and Functional Mouse Brain MRI (AIDAmri)

Magnetic resonance imaging (MRI) is a key technology in multimodal animal studies of brain connectivity and disease pathology. In vivo MRI provides non-invasive, whole brain macroscopic images containing structural and functional information, thereby complementing invasive in vivo high-resolution microscopy and ex vivo molecular techniques. Brain mapping, the correlation of corresponding regions between multiple brains in a standard brain atlas system, is widely used in human MRI. For small animal MRI, however, there is no scientific consensus on pre-processing strategies and atlas-based neuroinformatics. Thus, it remains difficult to compare and validate results from different pre-clinical studies which were processed using custom-made code or individual adjustments of clinical MRI software and without a standard brain reference atlas. Here, we describe AIDAmri, a novel Atlas-based Imaging Data Analysis pipeline to process structural and functional mouse brain data including anatomical MRI, fiber tracking using diffusion tensor imaging (DTI) and functional connectivity analysis using resting-state functional MRI (rs-fMRI). The AIDAmri pipeline includes automated pre-processing steps, such as raw data conversion, skull-stripping and bias-field correction as well as image registration with the Allen Mouse Brain Reference Atlas (ARA). Following a modular structure developed in Python scripting language, the pipeline integrates established and newly developed algorithms. Each processing step was optimized for efficient data processing requiring minimal user-input and user programming skills. The raw data is analyzed and results transferred to the ARA coordinate system in order to allow an efficient and highly-accurate region-based analysis. AIDAmri is intended to fill the gap of a missing open-access and cross-platform toolbox for the most relevant mouse brain MRI sequences thereby facilitating data processing in large cohorts and multi-center studies.

Denoising high angular resolution diffusion imaging data by combining singular value decomposition and non-local means filter

BACKGROUND

High angular resolution diffusion imaging (HARDI) data is typically corrupted with Rician noise. Although larger b-values help to retrieve more accurate angular diffusivity information, they also lead to an increase in noise generation.

NEW METHOD

In order to sufficiently reduce noise in HARDI images and improve the construction of orientation distribution function (ODF) fields, a novel denoising method was developed in this study by combining the singular value decomposition (SVD) and non-local means (NLM) filter. Similar 3D patches were first recruited into a matrix from a search volume. HARDI signals in the matrix were then re-estimated using the SVD low rank approximation, and a NLM filter was employed to filter out any residual noise.

RESULTS

The performance of the proposed method was evaluated against the state-of-the-art denoising methods based on both synthetic and real HARDI datasets. Results demonstrated the superior performance of the developed SVD-NLM method in denoising HARDI data through preserving fine angular structural details and estimating diffusion orientations from improved ODF fields.

CONCLUSION

The proposed SVD-NLM method can improve HARDI quantitative computations, such as MRI brain tissue segmentation and diffusion profile estimation, that rely on the quality of imaging data.

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.

A decomposition model and voxel selection framework for fMRI analysis to predict neural response of visual stimuli

This paper presents an fMRI signal analysis methodology using geometric mean curve decomposition (GMCD) and mutual information-based voxel selection framework. Previously, the fMRI signal analysis has been conducted using empirical mean curve decomposition (EMCD) model and voxel selection on raw fMRI signal. The erstwhile methodology loses frequency component, while the latter methodology suffers from signal redundancy. Both challenges are addressed by our methodology in which the frequency component is considered by decomposing the raw fMRI signal using geometric mean rather than arithmetic mean and the voxels are selected from EMCD signal using GMCD components, rather than raw fMRI signal. The proposed methodologies are adopted for predicting the neural response. Experimentations are conducted in the openly available fMRI data of six subjects, and comparisons are made with existing decomposition models and voxel selection frameworks. Subsequently, the effect of degree of selected voxels and the selection constraints are analyzed. The comparative results and the analysis demonstrate the superiority and the reliability of the proposed methodology.

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.

CUDA-based acceleration and BPN-assisted automation of bilateral filtering for brain MR image restoration

PURPOSE

Bilateral filters have been substantially exploited in numerous magnetic resonance (MR) image restoration applications for decades. Due to the deficiency of theoretical basis on the filter parameter setting, empirical manipulation with fixed values and noise variance-related adjustments has generally been employed. The outcome of these strategies is usually sensitive to the variation of the brain structures and not all the three parameter values are optimal. This article is in an attempt to investigate the optimal setting of the bilateral filter, from which an accelerated and automated restoration framework is developed.

METHODS

To reduce the computational burden of the bilateral filter, parallel computing with the graphics processing unit (GPU) architecture is first introduced. The NVIDIA Tesla K40c GPU with the compute unified device architecture (CUDA) functionality is specifically utilized to emphasize thread usages and memory resources. To correlate the filter parameters with image characteristics for automation, optimal image texture features are subsequently acquired based on the sequential forward floating selection (SFFS) scheme. Subsequently, the selected features are introduced into the back propagation network (BPN) model for filter parameter estimation. Finally, the k-fold cross validation method is adopted to evaluate the accuracy of the proposed filter parameter prediction framework.

RESULTS

A wide variety of T1-weighted brain MR images with various scenarios of noise levels and anatomic structures were utilized to train and validate this new parameter decision system with CUDA-based bilateral filtering. For a common brain MR image volume of 256 × 256 × 256 pixels, the speed-up gain reached 284. Six optimal texture features were acquired and associated with the BPN to establish a "high accuracy" parameter prediction system, which achieved a mean absolute percentage error (MAPE) of 5.6%. Automatic restoration results on 2460 brain MR images received an average relative error in terms of peak signal-to-noise ratio (PSNR) less than 0.1%. In comparison with many state-of-the-art filters, the proposed automation framework with CUDA-based bilateral filtering provided more favorable results both quantitatively and qualitatively.

CONCLUSIONS

Possessing unique characteristics and demonstrating exceptional performances, the proposed CUDA-based bilateral filter adequately removed random noise in multifarious brain MR images for further study in neurosciences and radiological sciences. It requires no prior knowledge of the noise variance and automatically restores MR images while preserving fine details. The strategy of exploiting the CUDA to accelerate the computation and incorporating texture features into the BPN to completely automate the bilateral filtering process is achievable and validated, from which the best performance is reached.

INFOS: spectrum fitting software for NMR analysis

Software for fitting of NMR spectra in MATLAB is presented. Spectra are fitted in the frequency domain, using Fourier transformed lineshapes, which are derived using the experimental acquisition and processing parameters. This yields more accurate fits compared to common fitting methods that use Lorentzian or Gaussian functions. Furthermore, a very time-efficient algorithm for calculating and fitting spectra has been developed. The software also performs initial peak picking, followed by subsequent fitting and refinement of the peak list, by iteratively adding and removing peaks to improve the overall fit. Estimation of error on fitting parameters is performed using a Monte-Carlo approach. Many fitting options allow the software to be flexible enough for a wide array of applications, while still being straightforward to set up with minimal user input.

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.

A partial differential equation-based general framework adapted to Rayleigh's, Rician's and Gaussian's distributed noise for restoration and enhancement of magnetic resonance image

The proposed framework is obtained by casting the noise removal problem into a variational framework. This framework automatically identifies the various types of noise present in the magnetic resonance image and filters them by choosing an appropriate filter. This filter includes two terms: the first term is a data likelihood term and the second term is a prior function. The first term is obtained by minimizing the negative log likelihood of the corresponding probability density functions: Gaussian or Rayleigh or Rician. Further, due to the ill-posedness of the likelihood term, a prior function is needed. This paper examines three partial differential equation based priors which include total variation based prior, anisotropic diffusion based prior, and a complex diffusion (CD) based prior. A regularization parameter is used to balance the trade-off between data fidelity term and prior. The finite difference scheme is used for discretization of the proposed method. The performance analysis and comparative study of the proposed method with other standard methods is presented for brain web dataset at varying noise levels in terms of peak signal-to-noise ratio, mean square error, structure similarity index map, and correlation parameter. From the simulation results, it is observed that the proposed framework with CD based prior is performing better in comparison to other priors in consideration.

Dual-domain denoising in three dimensional magnetic resonance imaging

Denoising is a crucial preprocessing procedure for three dimensional magnetic resonance imaging (3D MRI). Existing denoising methods are predominantly implemented in a single domain, ignoring information in other domains. However, denoising methods are becoming increasingly complex, making analysis and implementation challenging. The present study aimed to develop a dual-domain image denoising (DDID) algorithm for 3D MRI that encapsulates information from the spatial and transform domains. In the present study, the DDID method was used to distinguish signal from noise in the spatial and frequency domains, after which robust accurate noise estimation was introduced for iterative filtering, which is simple and beneficial for computation. In addition, the proposed method was compared quantitatively and qualitatively with existing methods for synthetic and in vivo MRI datasets. The results of the present study suggested that the novel DDID algorithm performed well and provided competitive results, as compared with existing MRI denoising filters.

In Vivo Fate Imaging of Intracerebral Stem Cell Grafts in Mouse Brain

We generated transgenic human neural stem cells (hNSCs) stably expressing the reporter genes Luciferase for bioluminescence imaging (BLI) and GFP for fluorescence imaging, for multimodal imaging investigations. These transgenic hNSCs were further labeled with a clinically approved perfluoropolyether to perform parallel ¹⁹F MRI studies. In vitro validation demonstrated normal cell proliferation and differentiation of the transgenic and additionally labeled hNSCs, closely the same as the wild type cell line, making them suitable for in vivo application. Labeled and unlabeled transgenic hNSCs were implanted into the striatum of mouse brain. The time profile of their cell fate after intracerebral grafting was monitored during nine days following implantation with our multimodal imaging approach, assessing both functional and anatomical condition. The ¹⁹F MRI demarcated the graft location and permitted to estimate the cell number in the graft. BLI showed a pronounce cell loss during this monitoring period, indicated by the decrease of the viability signal. The in vivo obtained cell fate results were further validated and confirmed by immunohistochemistry. We could show that the surviving cells of the graft continued to differentiate into early neurons, while the severe cell loss could be explained by an inflammatory reaction to the graft, showing the graft being surrounded by activated microglia and macrophages. These results are different from earlier cell survival studies of our group where we had implanted the identical cells into the same mouse strain but in the cortex and not in the striatum. The cortical transplanted cells did not show any loss in viability but only pronounced and continuous neuronal differentiation.

Impact of the calculation algorithm on biexponential fitting of diffusion-weighted MRI in upper abdominal organs

PURPOSE

To compare the variability, precision, and accuracy of six different algorithms (Levenberg-Marquardt, Trust-Region, Fixed-Dp , Segmented-Unconstrained, Segmented-Constrained, and Bayesian-Probability) for computing intravoxel-incoherent-motion-related parameters in upper abdominal organs.

METHODS

Following the acquisition of abdominal diffusion-weighted magnetic resonance images of 10 healthy men, six distinct algorithms were employed to compute intravoxel-incoherent-motion-related parameters in the left and right liver lobe, pancreas, spleen, renal cortex, and renal medulla. Algorithms were evaluated regarding inter-reader and intersubject variability. Comparability of results was assessed by analyses of variance. The algorithms' precision and accuracy were investigated on simulated data.

RESULTS

A Bayesian-Probability based approach was associated with very low inter-reader variability (average Intraclass Correlation Coefficients: 96.5-99.6%), the lowest inter-subject variability (Coefficients of Variation [CV] for the pure diffusion coefficient Dt : 3.8% in the renal medulla, 6.6% in the renal cortex, 10.4-12.1% in the left and right liver lobe, 15.3% in the spleen, 15.8% in the pancreas; for the perfusion fraction Fp : 15.5% on average; for the pseudodiffusion coefficient Dp : 25.8% on average), and the highest precision and accuracy. Results differed significantly (P < 0.05) across algorithms in all anatomical regions.

CONCLUSION

The Bayesian-Probability algorithm should be preferred when computing intravoxel-incoherent-motion-related parameters in upper abdominal organs.

Detecting statistically significant differences in quantitative MRI experiments, applied to diffusion tensor imaging

In this work we present a framework for reliably detecting significant differences in quantitative magnetic resonance imaging and evaluate it with diffusion tensor imaging (DTI) experiments. As part of this framework we propose a new spatially regularized maximum likelihood estimator that simultaneously estimates the quantitative parameters and the spatially-smoothly-varying noise level from the acquisitions. The noise level estimation method does not require repeated acquisitions. We show that the amount of regularization in this method can be set a priori to achieve a desired coefficient of variation of the estimated noise level. The noise level estimate allows the construction of a Cramér-Rao-lower-bound based test statistic that reliably assesses the significance of differences between voxels within a scan or across different scans. We show that the regularized noise level estimate improves upon existing methods and results in a substantially increased precision of the uncertainty estimates of the DTI parameters. It enables correct specification of the null distribution of the test statistic and with it the test statistic obtains the highest sensitivity and specificity. The source code of the estimation framework, test statistic and experiment scripts are made available to the community.

Spatially variant noise estimation in MRI: a homomorphic approach

The reliable estimation of noise characteristics in MRI is a task of great importance due to the influence of noise features in extensively used post-processing algorithms. Many methods have been proposed in the literature to retrieve noise features from the magnitude signal. However, most of them assume a stationary noise model, i.e., the features of noise do not vary with the position inside the image. This assumption does not hold when modern scanning techniques are considered, e.g., in the case of parallel reconstruction and intensity correction. Therefore, new noise estimators must be found to cope with non-stationary noise. Some methods have been recently proposed in the literature. However, they require multiple acquisitions or extra information which is usually not available (biophysical models, sensitivity of coils). In this work we overcome this drawback by proposing a new method that can accurately estimate the non-stationary parameters of noise from just a single magnitude image. In the derivation, we considered the noise to follow a non-stationary Rician distribution, since it is the most common model in real acquisitions (e.g., SENSE reconstruction), though it can be easily generalized to other models. The proposed approach makes use of a homomorphic separation of the spatially variant noise in two terms: a stationary noise term and one low frequency signal that correspond to the x-dependent variance of noise. The non-stationary variance of noise is then estimated by a low pass filtering with a Rician bias correction. Results in real and synthetic experiments evidence the better performance and the lowest error variance of the proposed methodology when compared to the state-of-the-art methods.

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.

A framework for accurate determination of the T₂ distribution from multiple echo magnitude MRI images

Measurement of the T2 distribution in tissues provides biologically relevant information about normal and abnormal microstructure and organization. Typically, the T2 distribution is obtained by fitting the magnitude MR images acquired by a multi-echo MRI pulse sequence using an inverse Laplace transform (ILT) algorithm. It is well known that the ideal magnitude MR signal follows a Rician distribution. Unfortunately, studies attempting to establish the validity and efficacy of the ILT algorithm assume that these input signals are Gaussian distributed. Violation of the normality (or Gaussian) assumption introduces unexpected artifacts, including spurious cerebrospinal fluid (CSF)-like long T2 components; bias of the true geometric mean T2 values and in the relative fractions of various components; and blurring of nearby T2 peaks in the T2 distribution. Here we apply and extend our previously proposed magnitude signal transformation framework to map noisy Rician-distributed magnitude multi-echo MRI signals into Gaussian-distributed signals with high accuracy and precision. We then perform an ILT on the transformed data to obtain an accurate T2 distribution. Additionally, we demonstrate, by simulations and experiments, that this approach corrects the aforementioned artifacts in magnitude multi-echo MR images over a large range of signal-to-noise ratios.

Iterative reweighted linear least squares for accurate, fast, and robust estimation of diffusion magnetic resonance parameters

PURPOSE

Diffusion-weighted magnetic resonance imaging suffers from physiological noise, such as artifacts caused by motion or system instabilities. Therefore, there is a need for robust diffusion parameter estimation techniques. In the past, several techniques have been proposed, including RESTORE and iRESTORE (Chang et al. Magn Reson Med 2005; 53:1088-1095; Chang et al. Magn Reson Med 2012; 68:1654-1663). However, these techniques are based on nonlinear estimators and are consequently computationally intensive.

METHOD

In this work, we present a new, robust, iteratively reweighted linear least squares (IRLLS) estimator. IRLLS performs a voxel-wise identification of outliers in diffusion-weighted magnetic resonance images, where it exploits the natural skewness of the data distribution to become more sensitive to both signal hyperintensities and signal dropouts.

RESULTS

Both simulations and real data experiments were conducted to compare IRLLS with other state-of-the-art techniques. While IRLLS showed no significant loss in accuracy or precision, it proved to be substantially faster than both RESTORE and iRESTORE. In addition, IRLLS proved to be even more robust when considering the overestimation of the noise level or when the signal-to-noise ratio is low.

CONCLUSION

The substantially shortened calculation time in combination with the increased robustness and accuracy, make IRLLS a practical and reliable alternative to current state-of-the-art techniques for the robust estimation of diffusion-weighted magnetic resonance parameters.

Denoising diffusion-weighted magnitude MR images using rank and edge constraints

PURPOSE

To improve signal-to-noise ratio for diffusion-weighted magnetic resonance images.

METHODS

A new method is proposed for denoising diffusion-weighted magnitude images. The proposed method formulates the denoising problem as an maximum a posteriori} estimation problem based on Rician/noncentral χ likelihood models, incorporating an edge prior and a low-rank model. The resulting optimization problem is solved efficiently using a half-quadratic method with an alternating minimization scheme.

RESULTS

The performance of the proposed method has been validated using simulated and experimental data. Diffusion-weighted images and noisy data were simulated based on the diffusion tensor imaging model and Rician/noncentral χ distributions. The simulation study (with known gold standard) shows substantial improvements in single-to-noise ratio and diffusion tensor estimation after denoising. In vivo diffusion imaging data at different b-values were acquired. Based on the experimental data, qualitative improvement in image quality and quantitative improvement in diffusion tensor estimation were demonstrated. Additionally, the proposed method is shown to outperform one of the state-of-the-art nonlocal means-based denoising algorithms, both qualitatively and quantitatively.

CONCLUSION

The single-to-noise ratio of diffusion-weighted images can be effectively improved with rank and edge constraints, resulting in an improvement in diffusion parameter estimation accuracy.

Ricean over Gaussian modelling in magnitude fMRI Analysis-Added Complexity with Negligible Practical Benefits

It is well-known that Gaussian modeling of functional Magnetic Resonance Imaging (fMRI) magnitude time-course data, which are truly Rice-distributed, constitutes an approximation, especially at low signal-to-noise ratios (SNRs). Based on this fact, previous work has argued that Rice-based activation tests show superior performance over their Gaussian-based counterparts at low SNRs and should be preferred in spite of the attendant additional computational and estimation burden. Here, we revisit these past studies and after identifying and removing their underlying limiting assumptions and approximations, provide a more comprehensive comparison. Our experimental evaluations using ROC curve methodology show that tests derived using Ricean modeling are substantially superior over the Gaussian-based activation tests only for SNRs below 0.6, i.e SNR values far lower than those encountered in fMRI as currently practiced.

On the Expectation-Maximization Algorithm for Rice-Rayleigh Mixtures With Application to Noise Parameter Estimation in Magnitude MR Datasets

Magnitude magnetic resonance (MR) images are noise-contaminated measurements of the true signal, and it is important to assess the noise in many applications. A recently introduced approach models the magnitude MR datum at each voxel in terms of a mixture of upto one Rayleigh and an a priori unspecified number of Rice components, all with a common noise parameter. The Expectation-Maximization (EM) algorithm was developed for parameter estimation, with the mixing component membership of each voxel as the missing observation. This paper revisits the EM algorithm by introducing more missing observations into the estimation problem such that the complete (observed and missing parts) dataset can be modeled in terms of a regular exponential family. Both the EM algorithm and variance estimation are then fairly straightforward without any need for potentially unstable numerical optimization methods. Compared to local neighborhood- and wavelet-based noise-parameter estimation methods, the new EM-based approach is seen to perform well not only on simulation datasets but also on physical phantom and clinical imaging data.

An MRI denoising method using image data redundancy and local SNR estimation

This paper presents an LMMSE-based method for the three-dimensional (3D) denoising of MR images assuming a Rician noise model. Conventionally, the LMMSE method estimates the noise-less signal values using the observed MR data samples within local neighborhoods. This is not an efficient procedure to deal with this issue while the 3D MR data intrinsically includes many similar samples that can be used to improve the estimation results. To overcome this problem, we model MR data as random fields and establish a principled way which is capable of choosing the samples not only from a local neighborhood but also from a large portion of the given data. To follow the similar samples within the MR data, an effective similarity measure based on the local statistical moments of images is presented. The parameters of the proposed filter are automatically chosen from the estimated local signal-to-noise ratio. To further enhance the denoising performance, a recursive version of the introduced approach is also addressed. The proposed filter is compared with related state-of-the-art filters using both synthetic and real MR datasets. The experimental results demonstrate the superior performance of our proposal in removing the noise and preserving the anatomical structures of MR images.

Comprehensive framework for accurate diffusion MRI parameter estimation

During the last decade, many approaches have been proposed for improving the estimation of diffusion measures. These techniques have already shown an increase in accuracy based on theoretical considerations, such as incorporating prior knowledge of the data distribution. The increased accuracy of diffusion metric estimators is typically observed in well-defined simulations, where the assumptions regarding properties of the data distribution are known to be valid. In practice, however, correcting for subject motion and geometric eddy current deformations alters the data distribution tremendously such that it can no longer be expressed in a closed form. The image processing steps that precede the model fitting will render several assumptions on the data distribution invalid, potentially nullifying the benefit of applying more advanced diffusion estimators. In this work, we present a generic diffusion model fitting framework that considers some statistics of diffusion MRI data. A central role in the framework is played by the conditional least squares estimator. We demonstrate that the accuracy of that particular estimator can generally be preserved, regardless the applied preprocessing steps, if the noise parameter is known a priori. To fulfill that condition, we also propose an approach for the estimation of spatially varying noise levels.

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

Modern magnetic resonance (MR) imaging protocols based on multiple-coil acquisitions have carried on a new attention to noise and signal statistical modeling, as long as most of the existing techniques for data processing are model based. In particular, nonaccelerated multiple-coil and GeneRalized Autocalibrated Partially Parallel Acquisitions (GRAPPA) have brought noncentral-χ (nc-χ) statistics into stake as a suitable substitute for traditional Rician distributions. However, this model is only valid when the signals received by each coil are roughly uncorrelated. The recent literature on this topic suggests that this is often not the case, so nc-χ statistics are in principle not adequate. Fortunately, such model can be adapted through the definition of a set of effective parameters, namely, an effective noise power (greater than the actual power of thermal noise in the Radio Frequency receiver) and an effective number of coils (smaller than the actual number of RF receiving coils in the system). The implications of these artifacts in practical algorithms have not been discussed elsewhere. In the present paper, we aim to study their actual impact and suggest practical rules to cope with them. We define the main noise parameters in this context, introducing a new expression for the effective variance of noise which is of capital importance for the two image processing problems studied: first, we propose a new method to estimate the effective variance of noise from the composite magnitude signal of MR data when correlations are assumed. Second, we adapt several model-based image denoising techniques to the correlated case using the noise estimation techniques proposed. We show, through a number of experiments with synthetic, phantom, and in vivo data, that neglecting the correlated nature of noise in multiple-coil systems implies important errors even in the simplest cases. At the same time, the proper statistical characterization of noise through effective parameters drives to improved accuracy (both qualitatively and quantitatively) for both of the problems studied.

A CURE for noisy magnetic resonance images: chi-square unbiased risk estimation

n this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chisquare random variable. We then consider the task of denoising squared-magnitude magnetic resonance image data, which are well modeled as independent noncentral chi-square random variables on two degrees of freedom. We consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate, one in the general context of undecimated filterbank transforms, and another in the specific case of the unnormalized Haar wavelet transform. The resultant algorithms are computationally tractable and improve upon most state-of-the-art methods for both simulated and actual magnetic resonance image data.

Fractional-order time series models for extracting the haemodynamic response from functional magnetic resonance imaging data

The postprocessing of functional magnetic resonance imaging (fMRI) data to study the brain functions deals mainly with two objectives: signal detection and extraction of the haemodynamic response. Signal detection consists of exploring and detecting those areas of the brain that are triggered due to an external stimulus. Extraction of the haemodynamic response deals with describing and measuring the physiological process of activated regions in the brain due to stimulus. The haemodynamic response represents the change in oxygen levels since the brain functions require more glucose and oxygen upon stimulus that implies a change in blood flow. In the literature, different approaches to estimate and model the haemodynamic response have been proposed. These approaches can be discriminated in model structures that either provide a proper representation of the obtained measurements but provide no or a limited amount of physiological information, or provide physiological insight but lacks a proper fit to the data. In this paper, a novel model structure is studied for describing the haemodynamics in fMRI measurements: fractional models. We show that these models are flexible enough to describe the gathered data with the additional merit of providing physiological information.

What is the best way to estimate hospital quality outcomes? A simulation approach

OBJECTIVE

To test the accuracy of alternative estimators of hospital mortality quality using a Monte Carlo simulation experiment.

DATA SOURCES

Data are simulated to create an admission-level analytic dataset. The simulated data are validated by comparing distributional parameters (e.g., mean and standard deviation of 30-day mortality rate, hospital sample size) with the same parameters observed in Medicare data for acute myocardial infarction (AMI) inpatient admissions.

STUDY DESIGN

We perform a Monte Carlo simulation experiment in which true quality is known to test the accuracy of the Observed-over-Expected estimator, the Risk Standardized Mortality Rate (RSMR), the Dimick and Staiger (DS) estimator, the Hierarchical Poisson estimator, and the Moving Average estimator using hospital 30-day mortality for AMI as the outcome. Estimator accuracy is evaluated for all hospitals and for small, medium, and large hospitals.

DATA EXTRACTION METHODS

Data are simulated.

PRINCIPAL FINDINGS

Significant and substantial variation is observed in the accuracy of the tested outcome estimators. The DS estimator is the most accurate for all hospitals and for small hospitals using both accuracy criteria (root mean squared error and proportion of hospitals correctly classified into quintiles).

CONCLUSIONS

The mortality estimator currently in use by Medicare for public quality reporting, the RSMR, has been shown to be less accurate than the DS estimator, although the magnitude of the difference is not large. Pending testing and validation of our findings using current hospital data, CMS should reconsider the decision to publicly report mortality rates using the RSMR.

Spatially variable Rician noise in magnetic resonance imaging

Magnetic resonance images tend to be influenced by various random factors usually referred to as "noise". The principal sources of noise and related artefacts can be divided into two types: arising from hardware (acquisition coil arrays, gradient coils, field inhomogeneity); and arising from the subject (physiological noise including body motion, cardiac pulsation or respiratory motion). These factors negatively affect the resolution and reproducibility of the images. Therefore, a proper noise treatment is important for improving the performance of clinical and research investigations. Noise reduction becomes especially critical for the images with a low signal-to-noise ratio, such as those typically acquired in diffusion tensor imaging at high diffusion weightings. The standard methods of signal correction usually assume a uniform distribution of the standard deviation of the noise across the image and evaluate a single correction parameter for the whole image. We pursue a more advanced approach based on the assumption of an inhomogeneous distribution of noise in space and evaluate correction factors for each voxel individually. The Rician nature of the underlying noise is considered for low and high signal-to-noise ratios. The approach developed here has been examined using numerical simulations and in vivo brain diffusion tensor imaging experiments. The efficacy and usefulness of this approach is demonstrated here and the resultant effective tool is described.

Maximum likelihood estimation-based denoising of magnetic resonance images using restricted local neighborhoods

In this paper, we propose a method to denoise magnitude magnetic resonance (MR) images, which are Rician distributed. Conventionally, maximum likelihood methods incorporate the Rice distribution to estimate the true, underlying signal from a local neighborhood within which the signal is assumed to be constant. However, if this assumption is not met, such filtering will lead to blurred edges and loss of fine structures. As a solution to this problem, we put forward the concept of restricted local neighborhoods where the true intensity for each noisy pixel is estimated from a set of preselected neighboring pixels. To this end, a reference image is created from the noisy image using a recently proposed nonlocal means algorithm. This reference image is used as a prior for further noise reduction. A scheme is developed to locally select an appropriate subset of pixels from which the underlying signal is estimated. Experimental results based on the peak signal to noise ratio, structural similarity index matrix, Bhattacharyya coefficient and mean absolute difference from synthetic and real MR images demonstrate the superior performance of the proposed method over other state-of-the-art methods.

Modeling diffusion-weighted MRI as a spatially variant gaussian mixture: application to image denoising

PURPOSE

This work describes a spatially variant mixture model constrained by a Markov random field to model high angular resolution diffusion imaging (HARDI) data. Mixture models suit HARDI well because the attenuation by diffusion is inherently a mixture. The goal is to create a general model that can be used in different applications. This study focuses on image denoising and segmentation (primarily the former).

METHODS

HARDI signal attenuation data are used to train a Gaussian mixture model in which the mean vectors and covariance matrices are assumed to be independent of spatial locations, whereas the mixture weights are allowed to vary at different lattice positions. Spatial smoothness of the data is ensured by imposing a Markov random field prior on the mixture weights. The model is trained in an unsupervised fashion using the expectation maximization algorithm. The number of mixture components is determined using the minimum message length criterion from information theory. Once the model has been trained, it can be fitted to a noisy diffusion MRI volume by maximizing the posterior probability of the underlying noiseless data in a Bayesian framework, recovering a denoised version of the image. Moreover, the fitted probability maps of the mixture components can be used as features for posterior image segmentation.

RESULTS

The model-based denoising algorithm proposed here was compared on real data with three other approaches that are commonly used in the literature: Gaussian filtering, anisotropic diffusion, and Rician-adapted nonlocal means. The comparison shows that, at low signal-to-noise ratio, when these methods falter, our algorithm considerably outperforms them. When tractography is performed on the model-fitted data rather than on the noisy measurements, the quality of the output improves substantially. Finally, ventricle and caudate nucleus segmentation experiments also show the potential usefulness of the mixture probability maps for classification tasks.

CONCLUSIONS

The presented spatially variant mixture model for diffusion MRI provides excellent denoising results at low signal-to-noise ratios. This makes it possible to restore data acquired with a fast (i.e., noisy) pulse sequence to acceptable noise levels. This is the case in diffusion MRI, where a large number of diffusion-weighted volumes have to be acquired under clinical time constraints.