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36
WaveletBased Rician Noise Removal for Magnetic Resonance Imaging
, 1998
"... It is wellknown that the noise in magnetic resonance magnitude images obeys a Rician distribution. Unlike additive Gaussian noise, Rician noise is signaldependent and consequently separating signal from noise is a difficult task. Rician noise is especially problematic in low signaltonoise ratio ..."
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Cited by 94 (0 self)
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It is wellknown that the noise in magnetic resonance magnitude images obeys a Rician distribution. Unlike additive Gaussian noise, Rician noise is signaldependent and consequently separating signal from noise is a difficult task. Rician noise is especially problematic in low signaltonoise ratio (SNR) regimes where it not only causes random fluctuations, but also introduces a signaldependent bias to the data that reduces image contrast. This paper studies waveletdomain filtering methods for Rician noise removal. We derive a novel waveletdomain filter that adapts to variations in both the signal and the noise. The new waveletdomain filter reduces Rician noise contamination in both high and low SNR regimes. I. Introduction In magnetic resonance imaging (MRI), there is an intrinsic tradeoff between the signaltonoise ratio (SNR), spatial resolution, and acquisition time required by the intended clinical/research application [1]. Therefore, given physiological or research paradig...
MaximumLikelihood Estimation of Rician Distribution Parameters
 IEEE Transactions on Medical Imaging
, 1998
"... The problem of parameter estimation from Rician distributed data (e.g., magnitude magnetic resonance images) is addressed. The properties of conventional estimation methods are discussed and compared to maximumlikelihood (ML) estimation which is known to yield optimal results asymptotically. In con ..."
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Cited by 41 (4 self)
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The problem of parameter estimation from Rician distributed data (e.g., magnitude magnetic resonance images) is addressed. The properties of conventional estimation methods are discussed and compared to maximumlikelihood (ML) estimation which is known to yield optimal results asymptotically. In contrast to previously proposed methods, ML estimation is demonstrated to be unbiased for high signaltonoise ratio (SNR) and to yield physical relevant results for low SNR.
Maximum likelihood estimation of signal amplitude and noise variance from MR data. Magnetic Resonance in Medicine
, 2004
"... In magnetic resonance imaging, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian distributed noise. After applying an inverse Fourier transform the data remain complex valued and Gaussian distributed. If the signal amplitude is t ..."
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Cited by 22 (0 self)
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In magnetic resonance imaging, the raw data, which are acquired in spatial frequency space, are intrinsically complex valued and corrupted by Gaussian distributed noise. After applying an inverse Fourier transform the data remain complex valued and Gaussian distributed. If the signal amplitude is to be estimated, one has two options. It can be estimated directly from the complex valued data set, or one can first perform a magnitude operation on this data set, which changes the distribution of the data from Gaussian to Rician, and estimate the signal amplitude from the thus obtained magnitude image. Similarly, the noise variance can be estimated from both the complex and magnitude data sets. This paper addresses the question whether it is better to use complex valued data or magnitude data for the estimation of these parameters using the Maximum Likelihood method. As a performance criterion, the meansquared error (MSE) is used. 1
Noise and signal estimation in magnitude MRI and Rician distributed images: A LMMSE approach
 IEEE Xplore. Downloaded on October 14, 2008 at 13:00 from IEEE Xplore. Restrictions apply. et al.: RESTORATION OF DWI DATA USING A RICIAN LMMSE ESTIMATOR 1403
, 2008
"... Abstract—A new method for noise filtering in images that follow a Rician model—with particular attention to magnetic resonance imaging—is proposed. To that end, we have derived a (novel) closedform solution of the linear minimum mean square error (LMMSE) estimator for this distribution. Additionall ..."
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Cited by 21 (1 self)
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Abstract—A new method for noise filtering in images that follow a Rician model—with particular attention to magnetic resonance imaging—is proposed. To that end, we have derived a (novel) closedform solution of the linear minimum mean square error (LMMSE) estimator for this distribution. Additionally, a set of methods that automatically estimate the noise power are developed. These methods use information of the sample distribution of local statistics of the image, such as the local variance, the local mean, and the local mean square value. Accordingly, the dynamic estimation of noise leads to a recursive version of the LMMSE, which shows a good performance in both noise cleaning and feature preservation. This paper also includes the derivation of the probability density function of several local sample statistics for the Rayleigh and Rician model, upon which the estimators are built. Index Terms—Linear minimum mean square error (LMMSE) estimator, MRI filtering, noise estimation, Rician noise. I.
Introduction to diffusion tensor imaging mathematics
 Parts IIII, Concepts in Magnetic Resonance Part A
"... ABSTRACT: The mathematical aspects of diffusion tensor magnetic resonance imaging (DTMRI, or DTI), the measurement of the diffusion tensor by magnetic resonance imaging (MRI), are discussed in this threepart series. Part III begins with a comparison of different ways to calculate the tensor from d ..."
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Cited by 18 (0 self)
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ABSTRACT: The mathematical aspects of diffusion tensor magnetic resonance imaging (DTMRI, or DTI), the measurement of the diffusion tensor by magnetic resonance imaging (MRI), are discussed in this threepart series. Part III begins with a comparison of different ways to calculate the tensor from diffusionweighted imaging data. Next, the effects of noise on signal intensities and diffusion tensor measurements are discussed. In MRI signal intensities as well as DTI parameters, noise can introduce a bias (systematic deviation) as well as scatter (random deviation) in the data. Propagationoferror formulas are explained with examples. Stepbystep procedures for simulating diffusion tensor measurements are presented. Finally, methods for selecting the optimal b factor and number of b ϭ 0 images for measuring several properties of the diffusion tensor, including the trace (or mean diffusivity) and anisotropy, are presented.
Estimation of the noise in magnitude MR images
 Magnetic Resonance Imaging
, 1998
"... Magnitude Magnetic Resonance (MR) data are Rician distributed. In this note a new method is proposed to estimate the image noise variance for this type of data distribution. The method is based on a double image acquisition, thereby exploiting the knowledge of the Rice distribution moments. ..."
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Magnitude Magnetic Resonance (MR) data are Rician distributed. In this note a new method is proposed to estimate the image noise variance for this type of data distribution. The method is based on a double image acquisition, thereby exploiting the knowledge of the Rice distribution moments.
Estimation of signal and noise from Rician distributed data
, 1998
"... Conventional estimation methods applied to Rician distributed data, (such as magnitude magnetic resonance data) yield biased results. In our work, it is shown where the bias appears. Furthermore, a novel estimation technique, based on Maximum Likelihood estimation, is developed for optimal estimatio ..."
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Cited by 10 (2 self)
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Conventional estimation methods applied to Rician distributed data, (such as magnitude magnetic resonance data) yield biased results. In our work, it is shown where the bias appears. Furthermore, a novel estimation technique, based on Maximum Likelihood estimation, is developed for optimal estimation of signal as well as noise from Rician distributed data. It is shown that the proposed method is superior in terms of mean squared error compared to the performance of conventional estimation techniques.
Influence of multichannel combination, parallel imaging and other reconstruction techniques on MRI noise characteristics, Magnetic Resonance Imaging 26 (6
, 2008
"... Not for commercial sale or for any systematic external distribution by a third party ..."
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Not for commercial sale or for any systematic external distribution by a third party
RESEARCH Nonlinear filtering based on 3D wavelet transform for MRI denoising
"... Magnetic resonance (MR) images are normally corrupted by random noise which makes the automatic feature extraction and analysis of clinical data complicated. Therefore, denoising methods have traditionally been applied to improve MR image quality. In this study, we proposed a 3D extension of the wav ..."
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Magnetic resonance (MR) images are normally corrupted by random noise which makes the automatic feature extraction and analysis of clinical data complicated. Therefore, denoising methods have traditionally been applied to improve MR image quality. In this study, we proposed a 3D extension of the wavelet transform (WT)based bilateral filtering for Rician noise removal. Due to delineating capability of wavelet, 3D WT was employed to provide effective representation of the noisy coefficients. Bilateral filtering of the approximation coefficients in a modified neighborhood improved the denoising efficiency and effectively preserved the relevant edge features. Meanwhile, the detailed subbands were processed with an enhanced NeighShrink thresholding algorithm. Validation was performed on both simulated and real clinical data. Using the peak signaltonoise ratio (PSNR) to quantify the amount of noise of the MR images, we have achieved an average PSNR enhancement of 1.32 times with simulated data. The quantitative and the qualitative measures used as the quality metrics demonstrated the ability of the proposed method for noise cancellation.
Maximum Likelihood Estimators in Magnetic Resonance Imaging
"... Abstract. Images of the MRI signal intensity are normally constructed by taking the magnitude of the complexvalued data. This results in a biased estimate of the true signal intensity. We consider this as a problem of parameter estimation with a nuisance parameter. Using several standard techniques ..."
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Abstract. Images of the MRI signal intensity are normally constructed by taking the magnitude of the complexvalued data. This results in a biased estimate of the true signal intensity. We consider this as a problem of parameter estimation with a nuisance parameter. Using several standard techniques for this type of problem, we derive a variety of estimators for the MRI signal, some previously published and some novel. Using Monte Carlo experiments we compare the estimators we derive with others previously published. Our results suggest that one of the novel estimators we derive may strike a desirable tradeoff between bias and mean squared error. 1