Robust estimation of the noise variance from background MR data (original) (raw)
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Robust estimation of the noise variance from background MR data [6144-232]
In the literature, many methods are available for estimation of the variance of the noise in magnetic resonance (MR) images. A commonly used method, based on the maximum of the background mode of the histogram, is revisited and a new, robust, and easy to use method is presented based on maximum likelihood (ML) estimation. Both methods are evaluated in terms of accuracy and precision using simulated MR data. It is shown that the newly proposed method outperforms the commonly used method in terms of mean-squared error (MSE).
Automatic estimation of the noise variance from the histogram of a magnetic resonance image
Physics in Medicine and Biology, 2007
Estimation of the noise variance of a magnetic resonance (MR) image is important for various post-processing tasks. In the literature, various methods for noise variance estimation from MR images are available, most of them however requiring user interaction and/or multiple (perfectly aligned) images. In this paper, we focus on automatic histogram-based noise variance estimation techniques. Previously described methods are reviewed and a new method based on the maximum likelihood (ML) principle is presented. Using Monte Carlo simulation experiments as well as experimental MR data sets, the noise variance estimation methods are compared in terms of the root mean-squared error (RMSE). The results show that the newly proposed method is superior in terms of the RMSE. † Jan Sijbers is a Postdoctoral
Medical Imaging 2005: Image Processing, 2005
Signal intensity in magnetic resonance images (MRIs) is affected by random noise. Assessing noise-induced signal variance is important for controlling image quality. Knowledge of signal variance is required for correctly computing the chi-square value, a measure of goodness of fit, when fitting signal data to estimate quantitative parameters such as T1 and T2 relaxation times or diffusion tensor elements. Signal variance can be estimated from measurements of the noise variance in an object-and ghost-free region of the image background. However, identifying a large homogeneous region automatically is problematic. In this paper, a novel, fully automated approach for estimating the noise-induced signal variance in magnitude-reconstructed MRIs is proposed. This approach is based on the histogram analysis of the image signal intensity, explicitly by extracting the peak of the underlining Rayleigh distribution that would characterize the distribution of the background noise. The peak is extracted using a nonparametric univariate density estimation like the Parzen window density estimation; the corresponding peak position is shown here to be the expected signal variance in the object. The proposed method does not depend on prior foreground segmentation, and only one image with a small amount of background is required when the signal-to-noise ratio (SNR) is greater than three. This method is applicable to magnitude-reconstructed MRIs, though diffusion tensor (DT)-MRI is used here to demonstrate the approach.
Noise measurement from magnitude MRI using local estimates of variance and skewness
Physics in Medicine and Biology, 2010
In this note, we address the estimation of the noise level in magnitude magnetic resonance (MR) images in the absence of background data. Most of the methods proposed earlier exploit the Rayleigh distributed background region in MR images to estimate the noise level. These methods, however, cannot be used for images where no background information is available. In this note, we propose two different approaches for noise level estimation in the absence of the image background. The first method is based on the local estimation of the noise variance using maximum likelihood estimation and the second method is based on the local estimation of the skewness of the magnitude data distribution. Experimental results on synthetic and real MR image datasets show that the proposed estimators accurately estimate the noise level in a magnitude MR image, even without background data. (Some figures in this article are in colour only in the electronic version) Sijbers J and Dekker A J den 2004 Maximum likelihood estimation of signal amplitude and noise variance from MR data Magn. Reson. Med. 51 586-94 Sijbers J et al 1998 Maximum likelihood estimation of Rician distribution parameters IEEE Trans. Med. Imag. 17 357-61 Sijbers J et al 2007 Automatic estimation of the noise variance from the histogram of a magnetic resonance image Phys. Med. Biol. 52 1335-48 Zhang Y et al 2001 Segmentation of brain MR images through a hidden Markov random field model and the expectation maximization algorithm IEEE Trans. Med. Imaging 20 45-57
Segmentation Based Noise Variance Estimation from Background MRI Data
Lecture Notes in Computer Science, 2010
Accurate and precise estimation of the noise variance is often of key importance as an input parameter for posterior image processing tasks. In MR images, background data is well suited for noise estimation since (theoretically) it lacks contributions from object signal. However, background data not only suffers from small contributions of object signal but also from quantization of the intensity values. In this paper, we propose a noise variance estimation method that is insensitive to quantization errors and that is robust against low intensity variations such as low contrast tissues and ghost artifacts.
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.
About the background distribution in MR data: a local variance study
Magnetic Resonance Imaging, 2010
A model for the distribution of the sample local variance (SLV) of magnetic resonance data is proposed. It is based on a bimodal Gamma distribution, whose maxima are related to the signal and background areas of the image. The model is valid for single-and multiple-coil systems. The proposed distribution allows us to characterize some signal/background properties in MR data. As an example, the model is used to study the effect of the background size over noise estimation techniques and a method to test the validity of background-based noise estimators is presented.
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 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.
Medical Physics, 2010
The region-of-interest ͑ROI͒ selection and evaluation is one of the key factors in the successful evaluation of radiological images. However, the presence of noise in images may lead to incorrect diagnosis. The aim of this study was to test the hypothesis that the weighting by error estimation in ROI assessment might significantly improve the validity of the results. Methods: As a model, the data maps of the transverse relaxation time constants ͑T 2 ͒ from patients who underwent a matrix-associated chondrocyte transplantation procedure on the femoral condyle were analyzed. Artificial noise with a Rician density probability distribution was added to each TE image. ROIs were processed either as a regular arithmetic mean or as a weighted mean, in which weighted coefficients were calculated with regard to fitting error estimates ͓coefficient of determination ͑R 2 ͒; root mean squared error ͑RMSE͒, mean absolute error ͑MSE͒, mean squared error ͑MAE͒, and chi-squared error ͑ 2 ͔͒. Results: The global T 2 values in repair tissue ͑meanϮ standard deviation, 62Ϯ 7 ms; range 51-70 ms͒ and in healthy cartilage ͑meanϮ SD, 49Ϯ 6 ms; range 40-60 ms͒ were significantly different ͑p Ͻ 0.001͒. With a 45% or greater decrease from the original SNR value ͑corresponding to a noise level of 35% of random value͒, the statistical significance was lost ͑P Ͼ 0.05͒; however, the use of the coefficient of determination ͑R 2 ͒ as a correction factor was able to maintain the p-value of Ͻ0.05 up to a 56% decrease from the original SNR value. Conclusions: The results of this study can prospectively be applied in a wide range of radiological imaging techniques in cases when error estimation is possible. Our analysis on MR images with artificially added noise showed that utilization of the correlation of determination ͑R 2 ͒ as a weighting parameter in ROI evaluation may significantly improve the differentiation between native and transplanted cartilage tissue in noisy images. This could be an added benefit in the non-invasive monitoring of the post-operative status of patients with cartilage transplants if the MR images are not ideal ͑e.g., lower field strength or lower SNR͒.