595 research outputs found
Automatic, fast and robust characterization of noise distributions for diffusion MRI
Knowledge of the noise distribution in magnitude diffusion MRI images is the
centerpiece to quantify uncertainties arising from the acquisition process. The
use of parallel imaging methods, the number of receiver coils and imaging
filters applied by the scanner, amongst other factors, dictate the resulting
signal distribution. Accurate estimation beyond textbook Rician or noncentral
chi distributions often requires information about the acquisition process
(e.g. coils sensitivity maps or reconstruction coefficients), which is not
usually available. We introduce a new method where a change of variable
naturally gives rise to a particular form of the gamma distribution for
background signals. The first moments and maximum likelihood estimators of this
gamma distribution explicitly depend on the number of coils, making it possible
to estimate all unknown parameters using only the magnitude data. A rejection
step is used to make the method automatic and robust to artifacts. Experiments
on synthetic datasets show that the proposed method can reliably estimate both
the degrees of freedom and the standard deviation. The worst case errors range
from below 2% (spatially uniform noise) to approximately 10% (spatially
variable noise). Repeated acquisitions of in vivo datasets show that the
estimated parameters are stable and have lower variances than compared methods.Comment: v2: added publisher DOI statement, fixed text typo in appendix A
Monte Carlo-based Noise Compensation in Coil Intensity Corrected Endorectal MRI
Background: Prostate cancer is one of the most common forms of cancer found
in males making early diagnosis important. Magnetic resonance imaging (MRI) has
been useful in visualizing and localizing tumor candidates and with the use of
endorectal coils (ERC), the signal-to-noise ratio (SNR) can be improved. The
coils introduce intensity inhomogeneities and the surface coil intensity
correction built into MRI scanners is used to reduce these inhomogeneities.
However, the correction typically performed at the MRI scanner level leads to
noise amplification and noise level variations. Methods: In this study, we
introduce a new Monte Carlo-based noise compensation approach for coil
intensity corrected endorectal MRI which allows for effective noise
compensation and preservation of details within the prostate. The approach
accounts for the ERC SNR profile via a spatially-adaptive noise model for
correcting non-stationary noise variations. Such a method is useful
particularly for improving the image quality of coil intensity corrected
endorectal MRI data performed at the MRI scanner level and when the original
raw data is not available. Results: SNR and contrast-to-noise ratio (CNR)
analysis in patient experiments demonstrate an average improvement of 11.7 dB
and 11.2 dB respectively over uncorrected endorectal MRI, and provides strong
performance when compared to existing approaches. Conclusions: A new noise
compensation method was developed for the purpose of improving the quality of
coil intensity corrected endorectal MRI data performed at the MRI scanner
level. We illustrate that promising noise compensation performance can be
achieved for the proposed approach, which is particularly important for
processing coil intensity corrected endorectal MRI data performed at the MRI
scanner level and when the original raw data is not available.Comment: 23 page
Non local spatial and angular matching : enabling higher spatial resolution diffusion MRI datasets through adaptive denoising
Diffusion magnetic resonance imaging (MRI) datasets suffer from low Signal-to-Noise Ratio (SNR), especially at high b-values. Acquiring data at high b-values contains relevant information and is now of great interest for microstructural and connectomics studies. High noise levels bias the measurements due to the non-Gaussian nature of the noise, which in turn can lead to a false and biased estimation of the diffusion parameters. Additionally, the usage of in-plane acceleration techniques during the acquisition leads to a spatially varying noise distribution, which depends on the parallel acceleration method implemented on the scanner. This paper proposes a novel diffusion MRI denoising technique that can be used on all existing data, without adding to the scanning time. We first apply a statistical framework to convert both stationary and non stationary Rician and non central Chi distributed noise to Gaussian distributed noise, effectively removing the bias. We then introduce a spatially and angular adaptive denoising technique, the Non Local Spatial and Angular Matching (NLSAM) algorithm. Each volume is first decomposed in small 4D overlapping patches, thus capturing the spatial and angular structure of the diffusion data, and a dictionary of atoms is learned on those patches. A local sparse decomposition is then found by bounding the reconstruction error with the local noise variance. We compare against three other state-of-the-art denoising methods and show quantitative local and connectivity results on a synthetic phantom and on an in-vivo high resolution dataset. Overall, our method restores perceptual information, removes the noise bias in common diffusion metrics, restores the extracted peaks coherence and improves reproducibility of tractography on the synthetic dataset. On the 1.2 mm high resolution in-vivo dataset, our denoising improves the visual quality of the data and reduces the number of spurious tracts when compared to the noisy acquisition. Our work paves the way for higher spatial resolution acquisition of diffusion MRI datasets, which could in turn reveal new anatomical details that are not discernible at the spatial resolution currently used by the diffusion MRI community
DTI denoising for data with low signal to noise ratios
Low signal to noise ratio (SNR) experiments in diffusion tensor imaging (DTI) give key information about tracking and anisotropy, e. g., by measurements with small voxel sizes or with high b values. However, due to the complicated and dominating impact of thermal noise such data are still seldom analysed. In this paper Monte Carlo simulations are presented which investigate the distributions of noise for different DTI variables in low SNR situations. Based on this study a strategy for the application of spatial smoothing is derived. Optimal prerequisites for spatial filters are unbiased, bell shaped distributions with uniform variance, but, only few variables have a statistics close to that. To construct a convenient filter a chain of nonlinear Gaussian filters is adapted to peculiarities of DTI and a bias correction is introduced. This edge preserving three dimensional filter is then validated via a quasi realistic model. Further, it is shown that for small sample sizes the filter is as effective as a maximum likelihood estimator and produces reliable results down to a local SNR of approximately 1. The filter is finally applied to very recent data with isotropic voxels of the size 1Ć1Ć1mm^3 which corresponds to a spatially mean SNR of 2.5. This application demonstrates the statistical robustness of the filter method. Though the Rician noise model is only approximately realized in the data, the gain of information by spatial smoothing is considerable
Automated characterization of noise distributions in diffusion MRI data
Knowledge of the noise distribution in diffusion MRI is the centerpiece to
quantify uncertainties arising from the acquisition process. Accurate
estimation beyond textbook distributions often requires information about the
acquisition process, which is usually not available. We introduce two new
automated methods using the moments and maximum likelihood equations of the
Gamma distribution to estimate all unknown parameters using only the magnitude
data. A rejection step is used to make the framework automatic and robust to
artifacts. Simulations were created for two diffusion weightings with parallel
imaging. Furthermore, MRI data of a water phantom with different combinations
of parallel imaging were acquired. Finally, experiments on freely available
datasets are used to assess reproducibility when limited information about the
acquisition protocol is available. Additionally, we demonstrated the
applicability of the proposed methods for a bias correction and denoising task
on an in vivo dataset. A generalized version of the bias correction framework
for non integer degrees of freedom is also introduced. The proposed framework
is compared with three other algorithms with datasets from three vendors,
employing different reconstruction methods. Simulations showed that assuming a
Rician distribution can lead to misestimation of the noise distribution in
parallel imaging. Results showed that signal leakage in multiband can also lead
to a misestimation of the noise distribution. Repeated acquisitions of in vivo
datasets show that the estimated parameters are stable and have lower
variability than compared methods. Results show that the proposed methods
reduce the appearance of noise at high b-value. The proposed algorithms herein
can estimate both parameters of the noise distribution automatically, are
robust to signal leakage artifacts and perform best when used on acquired noise
maps.Comment: v3: Peer reviewed version v2: Manuscript as submitted to Medical
image analysis v1: Manuscript as submitted to Magnetic resonance in medicin
Spatially regularized multi-exponential transverse relaxation times estimation from magnitude MRI images under Rician noise
International audienceSynopsis This work aims at improving the estimation of multi-exponential transverse relaxation times from noisy magnitude MRI images. A spatially regularized Maximum-Likelihood estimator accounting for the Rician distribution of the noise was introduced. This approach is compared to a Rician corrected least-square criterion with the introduction of spatial regularization. To deal with the large-scale optimization problem, a majoration-minimization approach was used, allowing the implementation of both the maximum-likelihood estimator and the spatial regularization. The importance of the regularization alongside the rician noise incorporation is shown both visually and numerically on magnitude MRI images acquired on fruit samples. Purpose Multi-exponential relaxation times and their associated amplitudes in an MRI image provide very useful information for assessing the constituents of the imaged sample. Typical examples are the detection of water compartments of plant tissues and the quanti cation of myelin water fraction for multiple sclerosis disease diagnosis. The estimation of the multi-exponential signal model from magnitude MRI images faces the problem of a relatively low signal to noise ratio (SNR), with a Rician distributed noise and a large-scale optimization problem when dealing with the entire image. Actually, maps are composed of coherent regions with smooth variations between neighboring voxels. This study proposes an e cient reconstruction method of values and amplitudes from magnitude images by incorporating this information in order to reduce the noise e ect. The main feature of the method is to use a regularized maximum likelihood estimator derived from a Rician likelihood and a Majorization-Minimization approach coupled with the Levenberg-Marquardt algorithm to solve the large-scale optimization problem. Tests were conducted on apples and the numerical results are given to illustrate the relevance of this method and to discuss its performances. Methods For each voxel of the MRI image, the measured signal at echo time is represented by a multi-exponential model: with The data are subject to an additive Gaussian noise in the complex domain and therefore magnitude MRI data follows a Rician distribution : is the rst kind modi ed Bessel function of order 0 and is the standard deviation of the noise which is usually estimated from the image background. For an MRI image with voxels, the model parameters are usually estimated by minimizing the least-squares (LS) criterion under the assumption of a Gaussian noise using nonlinear LS solvers such as Levenberg-Marquardt (LM). However, this approach does not yield satisfying results when applied to magnitude data. Several solutions to overcome this issue are proposed by adding a correction term to the LS criterion. In this study, the retained correction uses the expectation value of data model under the hypothesis of Rician distribution since it outperforms the other correction strategies: stands for the sum of squares. We refer to this method as Rician corrected LS (RCLS). A more direct way for solving this estimation problem is to use a maximum likelihood (ML) estimator which comes down to minimize: To solve this optimization problem when dealing with the entire image, a majorization-minimization (MM) technique was adopted. The resulting MM-ML algorithm is summarized in gure 1, the LM algorithm used in this method minimizes a set of LS criteria derived from the quadratic majorization strategy. A spatial regularization term based on a cost function was also added to both criteria (and) to ensure spatial smoothness of the estimated maps. In order to reduce the numerical complexity by maintaining variable separability between each voxel and it's neighboring voxels , the function is majorized by : where stands for the iteration number of the iterative optimization algorithm
Data augmentation in Rician noise model and Bayesian Diffusion Tensor Imaging
Mapping white matter tracts is an essential step towards understanding brain
function. Diffusion Magnetic Resonance Imaging (dMRI) is the only noninvasive
technique which can detect in vivo anisotropies in the 3-dimensional diffusion
of water molecules, which correspond to nervous fibers in the living brain. In
this process, spectral data from the displacement distribution of water
molecules is collected by a magnetic resonance scanner. From the statistical
point of view, inverting the Fourier transform from such sparse and noisy
spectral measurements leads to a non-linear regression problem. Diffusion
tensor imaging (DTI) is the simplest modeling approach postulating a Gaussian
displacement distribution at each volume element (voxel). Typically the
inference is based on a linearized log-normal regression model that can fit the
spectral data at low frequencies. However such approximation fails to fit the
high frequency measurements which contain information about the details of the
displacement distribution but have a low signal to noise ratio. In this paper,
we directly work with the Rice noise model and cover the full range of
-values. Using data augmentation to represent the likelihood, we reduce the
non-linear regression problem to the framework of generalized linear models.
Then we construct a Bayesian hierarchical model in order to perform
simultaneously estimation and regularization of the tensor field. Finally the
Bayesian paradigm is implemented by using Markov chain Monte Carlo.Comment: 37 pages, 3 figure
Random noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections
The empirical origin of random noise is described, its influence on DTI variables is illustrated by a review of numerical and in vivo studies supplemented by new simulations investigating high noise levels. A stochastic model of noise propagation is presented to structure noise impact in DTI. Finally, basics of voxelwise and spatial denoising procedures are presented. Recent denoising procedures are reviewed and consequences of the stochastic model for convenient denoising strategies are discussed
Spatial Smoothing for Diffusion Tensor Imaging with low Signal to Noise Ratios
Though low signal to noise ratio (SNR) experiments in DTI give key information about tracking and anisotropy, e.g. by measurements with very small voxel sizes, due to the complicated impact of thermal noise such experiments are up to now seldom analysed. In this paper Monte Carlo simulations are presented which investigate the random fields of noise for different DTI variables in low SNR situations. Based on this study a strategy for spatial smoothing, which demands essentially uniform noise, is derived. To construct a convenient filter the weights of the nonlinear Aurich chain are adapted to DTI. This edge preserving three dimensional filter is then validated in different variants via a quasi realistic model and is applied to very new data with isotropic voxels of the size 1x1x1 mm3 which correspond to a spatial mean SNR of approximately 3
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