Informed RESTORE: A method for robust estimation of diffusion tensor from low redundancy datasets in the presence of physiological noise artifacts

Abstract

Physiological noise artifacts, especially those originating from cardiac pulsation and subject motion, are common in clinical Diffusion tensor-MRI acquisitions. Previous works show that signal perturbations produced by 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) method has been shown to be an effective strategy for improving tensor estimation on a voxel-by-voxel basis in the presence of artifactual data points in diffusion-weighted images. In this article, we address potential instabilities that may arise when using RESTORE and propose practical constraints to improve its usability. Moreover, we introduce a method, called informed RESTORE designed to remove physiological noise artifacts in datasets acquired with low redundancy (less than 30-40 diffusion-weighted image volumes)--a condition in which the original RESTORE algorithm may converge to an incorrect solution. This new method is based on the notion that physiological noise is more likely to result in signal dropouts than signal increases. Results from both Monte Carlo simulation and clinical diffusion data indicate that informed RESTORE performs very well in removing physiological noise artifacts for low redundancy diffusion-weighted image datasets.

Fig. 1

Flow diagram of the RESTORE algorithm with added constraints.

Fig. 2

Flow diagram of the informed RESTORE algorithm.

Fig. 3

The estimated FA of a selected slice of human brain using (a) original RESTORE algorithm and (b) RESTORE algorithm with added constraints. The bright voxels indicated by white arrows are caused by excluding too many DWI data points from the fitting.

Fig. 4

The standard error of computed signal standard deviation using the Walker, RMAD, and RRMAD methods with (a) one corrupted image, (b) two corrupted images, and (c) three corrupted images. The corrupted signal intensity values are set to be the original signal intensity values multiplied by the corruption factors. The different corruption factors ranging from 0.30 to 1.70 simulated different types and severity level of artifacts.

Fig. 5

Trace(D) and fractional anisotropy (FA) distributions for an isotropic diffusion tensor obtained from Monte Carlo simulated data with a 30 gradient direction scheme using the nonlinear least-squares method (blue), the RESTORE method with constraints (light green), and the iRESTORE method (dark green). Corrupted data points had their intensity values set to the original signal intensity values multiplied by 0.50. Outlier percentage is 20% for all plots. The red curve shows the true Trace(D) and FA distributions when there are no outliers in the DWIs.

Fig. 6

Trace(D) and fractional anisotropy (FA) distributions for an anisotropic diffusion tensor obtained from Monte Carlo simulated data with a 30 gradient direction scheme using the nonlinear least-squares method (blue), the RESTORE method with constraints (light green), and the iRESTORE method (dark green). Corrupted data points had their intensity values set to the original signal intensity values multiplied by 0.50. Outlier percentage is 20% for all plots. The red curve shows the true Trace(D) and FA distributions when there are no outliers in the DWIs.

Fig. 7

A non-cardiac gated low redundancy DTI data set using the basic six directions with four repeats. Physiological artifacts occurred in three repeats (replicate 1, 2, and 3), which is 75% of DWIs in one of the sampling directions.

Fig. 8

The DEC map obtained from the NLS, RESTORE with added constraints and informed RESTORE methods using the non-cardiac gated low redundancy DTI data set shown in figure 7.