Magnitude MR Images Research Articles

Simulating rigid head motion artifacts on brain magnitude MRI data-Outcome on image quality and segmentation of the cerebral cortex.

Magnetic Resonance Imaging (MRI) datasets from epidemiological studies often show a lower prevalence of motion artifacts than what is encountered in clinical practice. These artifacts can be unevenly distributed between subject groups and studies which introduces a bias that needs addressing when augmenting data for machine learning purposes. Since unreconstructed multi-channel k-space data is typically not available for population-based MRI datasets, motion simulations must be performed using signal magnitude data. There is thus a need to systematically evaluate how realistic such magnitude-based simulations are. We performed magnitude-based motion simulations on a dataset (MR-ART) from 148 subjects in which real motion-corrupted reference data was also available. The similarity of real and simulated motion was assessed by using image quality metrics (IQMs) including Coefficient of Joint Variation (CJV), Signal-to-Noise-Ratio (SNR), and Contrast-to-Noise-Ratio (CNR). An additional comparison was made by investigating the decrease in the Dice-Sørensen Coefficient (DSC) of automated segmentations with increasing motion severity. Segmentation of the cerebral cortex was performed with 6 freely available tools: FreeSurfer, BrainSuite, ANTs, SAMSEG, FastSurfer, and SynthSeg+. To better mimic the real subject motion, the original motion simulation within an existing data augmentation framework (TorchIO), was modified. This allowed a non-random motion paradigm and phase encoding direction. The mean difference in CJV/SNR/CNR between the real motion-corrupted images and our modified simulations (0.004±0.054/-0.7±1.8/-0.09±0.55) was lower than that of the original simulations (0.015±0.061/0.2±2.0/-0.29±0.62). Further, the mean difference in the DSC between the real motion-corrupted images was lower for our modified simulations (0.03±0.06) compared to the original simulations (-0.15±0.09). SynthSeg+ showed the highest robustness towards all forms of motion, real and simulated. In conclusion, reasonably realistic synthetic motion artifacts can be induced on a large-scale when only magnitude MR images are available to obtain unbiased data sets for the training of machine learning based models.

A tailored passive driver for liver MRE in pediatric patients.

Magnetic resonance elastography (MRE) is increasingly used in the pediatric population for diagnosis and staging of liver fibrosis. However, the MR-compatible driver and sequences are usually those used for adult patients. Our feasibility study aimed to adapt the standardized adult MRE passive driver and vibrational parameters to a pediatric population. We designed an elliptic passive driver shaped on a torus equipped with an elastic membrane and adapted to children's morphologies. As a first step, eight children (aged 8-18 years) were enrolled in a prospective pilot study aiming to determine the threshold vibrational amplitude for MRE using a custom passive driver, based on phase aliasing assessment and the occurrence of signal void artifacts on magnitude MR images. In the second step, the practicality and the consistency of the custom driver were assessed in a further 11 pediatric patients (aged 7-18 years). In the third step, we compared our custom driver vs. the commercial driver on six adult volunteers, in terms of the reliable region of interest area within the acquired MRE slices, the shear wave maps' quality, and measured stiffness values obtained. Based on pediatric patient data, the threshold vibrational amplitude expressed as percentage of maximum output was found to be 0.4 and 1.1 times the body weight (kg) at 40 and 60 Hz frequencies, respectively. In comparison to the commercial passive driver, the custom driver improved threefold the contact with the body surface, also enabling a more comfortable examination as self-assessed by the volunteers. Our custom driver was more comfortable for the volunteers and was able to generate more homogenous shear waves, yielding larger usable hepatic area, and more reliable stiffness values.

Estimation of Nonhomogeneous Noise in 2D Magnetic Resonance Imaging

AbstractMagnetic resonance images are often influenced by noise. Reliable estimation of noise characteristics is important for image post‐processing. The benchmark algorithms often assume a uniform noise model across the image; that is, the noise features are spatially invariant. A few noise estimators are found to cope with nonhomogeneous noise; however, they either require multiple acquisitions or other additional information. In this research work, we develop a method that can accurately estimate the nonhomogeneous parameters of noise from just a single magnitude image. The proposed algorithm is a two‐step approach. In the first step, we evaluate the standard deviation of noise assuming that it follows Gaussian distribution. This step utilizes a hybrid of spatial domain edge information suppression and transforms domain coefficient statistics to estimate a single value of standard deviation of noise in magnitude MR images. In the second step, the evaluated noise is corrected using the analytical expression that establishes the relationship between Gaussian noise and Rician noise. Results on synthetic and clinical data evidence the better performance of the proposed algorithm when compared to the benchmark methods.

Noise estimation in 2D MRI using DWT coefficients and optimized neural network

Robust estimation of noise strength in Magnetic Resonance Images (MRIs) is a task of great importance due to its extensive applications in image post-processing techniques. Many noise estimation algorithms have been proposed in the past to retrieve noise characteristics of the magnitude image. These algorithms rely on either the spatial or transform domain information of the image. In this research article, we propose a noise estimation algorithm that utilizes a hybrid Discrete Wavelet Transform (DWT) and edge information suppression based algorithm to estimate the strength of noise in magnitude MR images. The wavelet coefficients corresponding to spatial domain edges are eliminated using a down-sampled complement of the Sobel edge map. The distribution of average noise energy in spatial and transform domain which follows Parseval’s theorem is utilized for calculating the initial noise estimate. Further, the robustness of the proposed algorithm is enhanced using Feedforward Neural Network. The proposed algorithm is observed to be computationally fast and accurate. Results on synthetic and clinical T1- and T2-w brain MRIs following Gaussian or Rician distribution show better performance than the existing benchmark algorithms over a wide range of input noise.

Optimized bias and signal inference in diffusion-weighted image analysis (OBSIDIAN).

Correction of Rician signal bias in magnitude MR images. A model-based, iterative fitting procedure is used to simultaneously estimate true signal and underlying Gaussian noise with standard deviation on a pixel-by-pixel basis in magnitude MR images. A precomputed function that relates absolute residuals between measured signals and model fit to is used to iteratively estimate . The feasibility of the method is evaluated and compared to maximum likelihood estimation (MLE) for diffusion signal decay simulations and diffusion-weighted images of the prostate considering 21 linearly spaced b-values from 0 to 3000s/mm2 . A multidirectional analysis was performed with publically available brain data. Model simulations show that the Rician bias correction algorithm is fast, with an accuracy and precision that is on par to model-based MLE and direct fitting in the case of pure Gaussian noise. Increased accuracy in parameter prediction in a low signal-to-noise ratio (SNR) scenario is ideally achieved by using a composite of multiple signal decays from neighboring voxels as input for the algorithm. For patient data, good agreement with high SNR reference data of diffusion in prostate is achieved. OBSIDIAN is a novel, alternative, simple to implement approach for rapid Rician bias correction applicable in any case where differences between true signal decay and underlying model function can be considered negligible in comparison to noise. The proposed composite fitting approach permits accurate parameter estimation even in typical clinical scenarios with low SNR, which significantly simplifies comparison of complex diffusion parameters among studies.

Adaptive Bayesian filtering based restoration of MR images

MR images contain noise and for quantitative clinical diagnosis restoration is essential. For single coil MR images, noise follows Rician distribution when signal to noise ratio (SNR) is low and Gaussian distribution when SNR is high. Rician noise is signal dependent and introduces bias. The work proposes an adaptive Bayesian framework for restoration of 2D magnitude MR images. Restoration is achieved by Rician likelihood as the data attachment term with range and domain Gaussian filters, adaptive to noise as prior in Maximum A´ posterior framework. A good filtering behavior is achieved due to the domain component of the filter and crisp edges are preserved at the same time due to the noise adaptive range component. Rician likelihood aids the image restoration in terms of bias removal. Convergence of the proposed method further highlights the optimal filtering performance. Experiments conducted on publically available Brainweb phantom demonstrate enhanced performance in terms of signal to noise ratio, structural similarity index and overall performance.

Compressed Sensing-Based Simultaneous Recovery of Magnitude and Phase MR Images via Dual Trigonometric Sparsity

Complex-valued Magnetic Resonance Imaging (MRI) is widely used in clinical diagnosis. The magnitude images are mainly used for structure visualization, and the phase images reveal tissue properties, such as magnetic susceptibility and fluid flow information. While MRI is slow, compressed sensing (CS) can be used to reconstruct the accelerated acquisitions. Current CS-based MRI reconstruction algorithms mostly focus on magnitude image recovery, with less attention to the recovery of phase images. In this paper, we propose a novel CS algorithm to simultaneously recover the magnitude and phase MR images based on the sparsity of the trigonometric function. The CS method requires a sparse representation of the original images, and it is observed the trigonometric functions of phase images in the Wavelet domain promote sparsity. Therefore, rather than transforming the phase images directly into the Wavelet domain, we calculate the sine and cosine of the phase images whose Wavelet transforms are set as the L1-norm regularization term. The combination of the dual trigonometric functions captures a unique, faithful four-quadrant phase information, which also improves the reconstructed magnitude images through an alternating optimization procedure. Reconstructions of simulated images and in vivo images are studied, and both show the superiority of the proposed method over compared phase recovery algorithms.

Deep learning-based MR-to-CT synthesis: The influence of varying gradient echo-based MR images as input channels.

PurposeTo study the influence of gradient echo–based contrasts as input channels to a 3D patch‐based neural network trained for synthetic CT (sCT) generation in canine and human populations.MethodsMagnetic resonance images and CT scans of human and canine pelvic regions were acquired and paired using nonrigid registration. Magnitude MR images and Dixon reconstructed water, fat, in‐phase and opposed‐phase images were obtained from a single T1‐weighted multi‐echo gradient‐echo acquisition. From this set, 6 input configurations were defined, each containing 1 to 4 MR images regarded as input channels. For each configuration, a UNet‐derived deep learning model was trained for synthetic CT generation. Reconstructed Hounsfield unit maps were evaluated with peak SNR, mean absolute error, and mean error. Dice similarity coefficient and surface distance maps assessed the geometric fidelity of bones. Repeatability was estimated by replicating the training up to 10 times.ResultsSeventeen canines and 23 human subjects were included in the study. Performance and repeatability of single‐channel models were dependent on the TE‐related water–fat interference with variations of up to 17% in mean absolute error, and variations of up to 28% specifically in bones. Repeatability, Dice similarity coefficient, and mean absolute error were statistically significantly better in multichannel models with mean absolute error ranging from 33 to 40 Hounsfield units in humans and from 35 to 47 Hounsfield units in canines.ConclusionSignificant differences in performance and robustness of deep learning models for synthetic CT generation were observed depending on the input. In‐phase images outperformed opposed‐phase images, and Dixon reconstructed multichannel inputs outperformed single‐channel inputs.

Induced Current Magnetic Resonance Electrical Conductivity Imaging With Oscillating Gradients.

In this paper, induced current magnetic resonance electrical impedance tomography (ICMREIT) by means of current induction due to time-varying gradient fields of magnetic resonance imaging (MRI) systems is proposed. Eddy current and secondary magnetic flux density distributions are calculated for a numerical model composed of a z-gradient coil and a cylindrical conductor. An MRI pulse sequence is developed for the experimental evaluation of ICMREIT on a 3T MRI scanner. A relationship between the secondary magnetic flux density and the low-frequency (LF) MR phase is formulated. Characteristics of the LF phase, the eddy current, and the reconstructed conductivity distributions based on the simulated and the physical measurements are in agreement. Geometric shifts, which may contaminate the LF phase measurements, are not observed in the MR magnitude images. Low sensitivity of the LF phase measurements is a major limitation of ICMREIT towards clinical applications. The reconstructed conductivity images are rough estimates of true conductivity distribution of the experimental phantoms. Although the experimental results show that ICMREIT is safe and potentially applicable, its measurement sensitivity and reconstruction accuracy need to be optimized in order to improve the technique towards clinical applications.

Pressure Mapping and Hemodynamic Assessment of Intracranial Dural Sinuses and Dural Arteriovenous Fistulas with 4D Flow MRI.

The feasibility of 4D flow MR imaging to visualize flow patterns and generate relative pressure maps in the dural venous sinus in healthy subjects (n = 60) and patients with dural arteriovenous fistulas (n = 7) was investigated. Dural venous drainage was classified based on torcular Herophili anatomy by using 4D flow MR imaging-derived angiograms and magnitude images. Subjects were scanned in a 3T clinical MR imaging system. 4D flow MR imaging enabled noninvasive characterization of dural sinus anatomy and mapping of relative pressure differences.

Sensitivity analysis of magnetic field measurements for magnetic resonance electrical impedance tomography (MREIT).

Clinical use of magnetic resonance electrical impedance tomography (MREIT) still requires significant sensitivity improvements. Here, the measurement of the current-induced magnetic field (ΔBz,c ) is improved using systematic efficiency analyses and optimization of multi-echo spin echo (MESE) and steady-state free precession free induction decay (SSFP-FID) sequences. Considering T1 , T2 , and T2* relaxation in the signal-to-noise ratios (SNRs) of the MR magnitude images, the efficiency of MESE and SSFP-FID MREIT experiments, and its dependence on the sequence parameters, are analytically analyzed and simulated. The theoretical results are experimentally validated in a saline-filled homogenous spherical phantom with relaxation parameters similar to brain tissue. Measurement of ΔBz,c is also performed in a cylindrical phantom with saline and chicken meat. The efficiency simulations and experimental results are in good agreement. When using optimal parameters, ΔBz,c can be reliably measured in the phantom even at injected current strengths of 1 mA or lower for both sequence types. The importance of using proper crusher gradient selection on the phase evolution in a MESE experiment is also demonstrated. The efficiencies observed with the optimized sequence parameters will likely render in-vivo human brain MREIT feasible. Magn Reson Med 79:748-760, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

A computationally efficient non-local maximum likelihood estimation approach for Rician noise reduction in MRI

Magnetic resonance images are subjected to degradation due to the presence of noise from various sources. For further processing of the MR images and for effective visual analysis, the noise should be removed. Many denoising algorithms have been proposed for enhancing MR images. Preserving the structural details has its own importance in image denoising, and especially for medical images it should not be compromised. For effective image denoising, the data distribution in the images should be known in advance. Data in the magnitude MR images are Rician distributed (if acquired with single coil). Among the recently proposed denoising methods for reducing Rician noise, non-local maximum likelihood estimation method (NLML) proved to be an efficient one. But the superior performance of the NLML is restricted by its high computational complexity and non optimal way of selecting the samples for ML estimation. In this paper we address the above problems to some extend by introducing rotation invariant similarity measures. The proposed method aims to reduce the computational complexity and preserves the edges by discarding the dissimilar pixels by using a two-level refining approach. Comparative analysis of the proposed method with conventional NLML method based on the execution time and quantitative analysis in terms of PSNR, SSIM, FSIM and UIQI shows that the proposed method has an edge over the conventional method.

A two-step optimization approach for nonlocal total variation-based Rician noise reduction in magnetic resonance images.

Magnetic resonance imaging (MRI) often suffers from apparent noise during image acquisition and transmission. The degraded data can easily result in nonrobust postprocessing steps in medical image analysis. The purpose of this study is to eliminate noise effects and improve image quality using a nonlocal feature-preserving denoising method. From a statistical point of view, the magnitude MR images in the presence of noise are usually modeled using a Rician distribution. In the maximum a posteriori framework, a nonlocal total variation (NLTV)-based feature-preserving MRI Rician denoising model is proposed by taking full advantage of high degree of selfsimilarity and redundancy within MR images. However, the nonconvex data-fidelity term and nonsmooth NLTV regularizer make the denoising problem difficult to solve. To guarantee solution stability, a piecewise convex function is first introduced to approximate the nonconvex version. In what follows, a two-step optimization approach is developed to solve the resulting convex denoising model. In each step of this approach, the subproblem can be efficiently solved using existing optimization algorithms. The method performance is evaluated using synthetic and clinical MRI data sets as well as one diffusion tensor MRI (DTI) data set. Extensive experiments are conducted to compare the proposed method with several state-of-the-art denoising methods. For the synthetic and clinical MRI data sets, the proposed method considerably outperformed other competing denoising methods in terms of both quantitative and visual quality evaluations. It was capable of effectively removing noise in MR images and enhancing tissue characterization. The advantage of the proposed method became more significant as the noise level increased. For the DTI data set, compared with other denoising methods, the proposed method not only preserved the apparent diffusion coefficient but also generated more regular fractional anisotropy (FA) and color-coded FA without obvious visual artifacts. This study describes and validates a nonlocal feature-preserving method for Rician noise reduction on synthetic and real MRI data sets. By exploiting the feature-preserving capability of NLTV regularizer, the proposed method maintains a good balance between noise reduction and fine detail preservation. The experiments have demonstrated a huge potential of the proposed method for routine clinical practice.

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

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

Improving GRAPPA reconstruction by frequency discrimination in the ACS lines

GRAPPA is a well-known parallel imaging method that recovers the MR magnitude image from aliasing by using a weighted interpolation of the data in k-space. To estimate the optimal reconstruction weights, GRAPPA uses a band along the center of the k-space where the signal is sampled at the Nyquist rate, the so-called autocalibrated (ACS) lines. However, while the subsampled lines usually belong to the medium- to high-frequency areas of the spectrum, the ACS lines include the low-frequency areas around the DC component. The use for estimation and reconstruction of areas of the k-space with very different features may negatively affect the final reconstruction quality. We propose a simple, yet powerful method to eliminate reconstruction artifacts, based on the discrimination of the low-frequency spectrum. The proposal to improve the estimation of the weights lays on a proper selection of the coefficients within the ACS lines, which advises discarding those points around the DC component. A simple approach is the elimination of a square window in the center of the k-space, although more developed approaches can be used. The method is tested using real multiple-coil MRI acquisitions. We empirically show this approach achieves great enhancement rates, while keeping the same complexity of the original GRAPPA and reducing the g-factor. The reconstruction is even more accurate when combined with other reconstruction methods. Improvement rates of 35% are achieved for 32 ACS and acceleration rate of 3. The method proposed highly improves the accuracy of the GRAPPA coefficients and therefore the final image reconstruction. The method is fully compatible with the original GRAPPA formulation and with other optimization methods proposed in literature, and it can be easily implemented into the commercial scanning software.

Bayesian analysis of transverse signal decay with application to human brain.

Transverse relaxation analysis with several signal models has been used extensively to determine tissue and material properties. However, the derivation of corresponding parameter values is notoriously unreliable. We evaluate improvements in the quality of parameter estimation using Bayesian analysis and incorporating the Rician noise model, as appropriate for magnitude MR images. Monoexponential, stretched exponential, and biexponential signal models were analyzed using nonlinear least squares (NLLS) and Bayesian approaches. Simulations and phantom and human brain data were analyzed using three different approaches to account for noise. Parameter estimation bias (reflecting accuracy) and dispersion (reflecting precision) were derived for a range of signal-to-noise ratios (SNR) and relaxation parameters. All methods performed well at high SNR. At lower SNR, the Bayesian approach yielded parameter estimates of considerably greater precision, as well as greater accuracy, than did NLLS. Incorporation of the Rician noise model greatly improved accuracy and, to a somewhat lesser extent, precision, in derived transverse relaxation parameters. Analyses of data obtained from solution phantoms and from brain were consistent with simulations. Overall, estimation of parameters characterizing several different transverse relaxation models was markedly improved through use of Bayesian analysis and through incorporation of the Rician noise model.

Conductivity image enhancement in MREIT using adaptively weighted spatial averaging filter.

BackgroundIn magnetic resonance electrical impedance tomography (MREIT), we reconstruct conductivity images using magnetic flux density data induced by externally injected currents. Since we extract magnetic flux density data from acquired MR phase images, the amount of measurement noise increases in regions of weak MR signals. Especially for local regions of MR signal void, there may occur excessive amounts of noise to deteriorate the quality of reconstructed conductivity images. In this paper, we propose a new conductivity image enhancement method as a postprocessing technique to improve the image quality.MethodsWithin a magnetic flux density image, the amount of noise varies depending on the position-dependent MR signal intensity. Using the MR magnitude image which is always available in MREIT, we estimate noise levels of measured magnetic flux density data in local regions. Based on the noise estimates, we adjust the window size and weights of a spatial averaging filter, which is applied to reconstructed conductivity images. Without relying on a partial differential equation, the new method is fast and can be easily implemented.ResultsApplying the novel conductivity image enhancement method to experimental data, we could improve the image quality to better distinguish local regions with different conductivity contrasts. From phantom experiments, the estimated conductivity values had 80% less variations inside regions of homogeneous objects. Reconstructed conductivity images from upper and lower abdominal regions of animals showed much less artifacts in local regions of weak MR signals.ConclusionWe developed the fast and simple method to enhance the conductivity image quality by adaptively adjusting the weights and window size of the spatial averaging filter using MR magnitude images. Since the new method is implemented as a postprocessing step, we suggest adopting it without or with other preprocessing methods for application studies where conductivity contrast is of primary concern.

Adaptive Rician denoising with edge preservation for MR images of the articular cartilage

MR image offers better soft tissue contrast which makes it advantageous for cartilage diagnosis for patients suffering from Osteoarthritis. But magnitude MR images are susceptible to Rician noise which affects image quality leading to incorrect diagnosis. In this paper we propose a novel Rician denoising procedure with edge preservation capability. An adaptive filter with Brown–Forsythe statistical criterion has been implemented to avoid excessive filtering near the edges. Denoising is achieved using a linear minimum mean square estimate of the regional sample, obtained using a modified non-local means estimate within the neighbourhood of the image. The proposed filter was implemented on MR images of the knee, synthetic and a phantom. The efficiency of the denoising procedure was determined using signal-to-noise ratio, root mean square error, quality index based on local variance and contrast-to-noise ratio between true and denoised images of the cartilage. The method was also compared with other existing Rician denoising procedures and showed improved image contrast with edge preservation ability.

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.

Optimization of Bilateral Filter Parameters via Chi-Square Unbiased Risk Estimate

Bilateral filter is an edge-preserving diffusion filter and is widely used for image denoising. The denoising quality is sensitive to the choice of the bilateral filter parameters. Here, we propose to use the Chi-Square Unbiased Risk Estimate (CURE) for optimizing bilateral filter parameters in squared magnitude MR images, which follow a non-central chi-square distribution with two degrees of freedom. CURE is an unbiased estimate of the Mean Squared Error (MSE) and it does not require any knowledge of the noise-free data. We derive explicit analytical expressions for CURE in the setting of bilateral filters and present experimental results that confirm the optimality of CURE.