Abstract To improve the accuracy of tissue structural and architectural characterization with diffusion tensor imaging, an anisotropic smoothing algorithm is presented for reducing noise in diffusion tensor images efficiently and effectively. The presented algorithm is based on previous anisotropic diffusion filtering, which is implemented with a straightforward but inefficient explicit numerical scheme. The main contribution of this paper is to improve the performance of the previous method considerably by using unconditionally stable and second order time accurate semi-implicit scheme. Our new method needs only few or even one iteration to achieve better smoothed images than what is generated by tens of iterations of the previous method, which makes it more attractive to practical use. Experiments with simulated and in vivo data have demonstrated the advantage of our new algorithm for denoising diffusion tensor images in terms of efficiency and effectiveness. 1. Introduction Magnet resonance diffusion tensor imaging (DTI) has established to be a primary technique for non-invasive characterization of the structural and architectural features of living tissue [1]. As DTI is typically performed with echo-planar imaging sequences, the images acquired usually have very poor signal-to-noise ratio (SNR). High image noise is quite detrimental to accurate assessment of tissue property, most notably erroneous calculations of the principal diffusion direction [2] and an overestimate of fractional anisotropy (FA) due to sorting bias [3]. To improve SNR a plethora of image post processing techniques have been proposed for reducing noise in DTI data. These include non-linear diffusion filtering [4, 5], B- spline fitting [6] and more sophisticated regularization methods based on Markovian model [7], variational principles [8, 9], and Riemannian geometry [10], [11], [12]. This repository of smoothing techniques, however, has not established their practical utility due, in part, to the somewhat time-consuming iterative numerical implementation especially when the computation complexity increases with the number of weighting directions, or to a lack of rigorous validation with in vivo DTI data to prove their practical value. In this work we proposed a highly efficient and effective method for anisotropic smoothing of diffusion tensor images by using an unconditionally stable and second order accurate semi-implicit (Craig-Sneyd) scheme [17]. The unconditional stability allows the use of very large step sizes so that our scheme requires much fewer iterations and thus is more efficient than commonly used schemes to achieve a certain degree of smoothing. And second order time accuracy enables our scheme to reduce noise more effectively than first order schemes [15] with the same total iteration time 1 . Both efficiency and effectiveness are evaluated quantitatively with simulated and in vivo DTI data. The proposed scheme works specifically for the anisotropic smoothing [13] with tensor diffusivity that allows both image detail enhancement and noise reduction. Although there are other efficient and accurate schemes for scalar diffusivity driven diffusion filtering [15, 16], this is the first effort to apply unconditionally stable and second order accurate schemes to tensor diffusivity driven diffusion filtering. 2. Anisotropic Noise Reduction in Diffusion Tensor Images As implemented previously [13], noise in DTI data is reduced by anisotropically smoothing the diffusion weighted images (DWI) from which diffusion tensors are derived. The smoothing process is governed by the following diffusion equation: ( ) m m I T div t I ∇ ⋅ = ∂ ∂ (1) where m I is the image intensity in weighting direction m, 1 Total iteration time represents accumulated time in the diffusion equation and is a parameter determining the total amount of smoothing. Computation time mentioned later refers to the time consumed on computers. Diffusion Tensor Image Smoothing Using Efficient and Effective Anisotropic Filtering Qing Xu, Adam W. Anderson, John C. Gore and Zhaohua Ding Vanderbilt University Institute of Imaging Science, Vanderbilt University, 1161 21st Avenue South, Nashville, TN 37232-2310 Qing.xu.1@vanderbilt.edu 978-1-4244-1631-8/07/$25.00 ©2007 IEEE