A Study on the Comparison of Median Filter Regularization Methods in Diffusion Tensor MRI

Diffusion tensor magnetic resonance imaging (DT-MRI) is a method which makes it possible to study non-invasively the architecture of axonal fibers in the central nervous system. Since eigenvectors obtained from DT-MRI usually contain noise, the calculated vector directions may be deviated from the real fiber orientation. Therefore, noise errors can be accumulated as fiber tract becomes longer in tractography of DT-MRI. We used three algorithms for computing matrix medians which are the simple median method, the gradient descent method, and the successive Fermat method, because matrix-valued median filters show excellent capabilities for structure-preserving denoising. The results of the successive Fermat method give better than those of the simple median method and is faster and the performance is similar to those of the gradient descent method.