Diffusion tensor magnetic resonance imaging (DT-MRI) is increasingly used in clinical research and
applications for its ability to depict white matter tracts and for its sensitivity to microstructural and
architectural features of brain tissue. However, artifacts are common in clinical DT-MRI acquisitions.
Signal perturbations produced by such artifacts can be severe and neglecting to account for their
contribution can result in erroneous diffusion tensor values. The Robust Estimation of Tensors by Outlier
Rejection (RESTORE) has been demonstrated to be an effective method for improving tensor estimation
on a voxel-by-voxel basis in the presence of artifactual data points in diffusion weighted images. Despite
the very good performance of the RESTORE algorithm, there are some limitations and opportunities for
improvement. Instabilities in tensor estimation using RESTORE have been observed in clinical human
brain data. Those instabilities can come from the intrinsic high frequency spin inflow effects in non-DWIs
or from excluding too many data points from the fitting. This paper proposes several practical constraints
to the original RESTORE method. Results from Monte Carlo simulation indicate that the improved RESTORE method reduces the instabilities in tensor estimation observed from the original RESTORE method.
The longitudinal relaxation time, T<sub>1</sub>, can be estimated from two or more spoiled gradient recalled echo x
(SPGR) images with two or more flip angles and one or more repetition times (TRs). The function relating
signal intensity and the parameters are nonlinear; T<sub>1</sub> maps can be computed from SPGR signals using
nonlinear least squares regression. A widely-used linear method transforms the nonlinear model by
assuming a fixed TR in SPGR images. This constraint is not desirable since multiple TRs are a clinically
practical way to reduce the total acquisition time, to satisfy the required resolution, and/or to combine
SPGR data acquired at different times. A new linear least squares method is proposed using the first order
Taylor expansion. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy and
precision of the estimated T<sub>1</sub> from the proposed linear and the nonlinear methods. We show that the new
linear least squares method provides T<sub>1</sub> estimates comparable in both precision and accuracy to those from
the nonlinear method, allowing multiple TRs and reducing computation time significantly.
Proc. SPIE. 5747, Medical Imaging 2005: Image Processing
KEYWORDS: Signal to noise ratio, Magnetic resonance imaging, Image segmentation, Error analysis, Diffusion, Magnetism, Interference (communication), Data acquisition, Monte Carlo methods, Data analysis
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.