Impact of Diffusion Tensor Field Smoothing with Log-Cholesky Metric on Noise Reduction

Diffusion Tensor Imaging (DTI) is a noise-sensitive method, where a low Signal-to-Noise Ratio (SNR) results in significant errors in the estimated tensor field. Post-reconstruction tensor field smoothing is a simple and effective solution for alleviating this problem. Diffusion tensors can be represented by Symmetric Positive-Definite (SPD) matrices which can be viewed as a Riemannian manifold after defining a suitable metric on the space of SPD matrices. The Log-Cholesky metric is a recently developed concept with several advantages over previously defined metrics, e.g., Frobenius, Log-Euclidean, and affine-invariant metrics. In this work, we implemented a smoothing method based on the Log-Cholesky metric and show its effectiveness as a simple solution to filtering noisy diffusion tensor fields.