A robust variational approach for simultaneous smoothing and estimation of DTI

• Published in: NeuroImage (Orlando, Fla.) Vol. 67; pp. 33 - 41
• Main Authors: Liu, Meizhu, Vemuri, Baba C., Deriche, Rachid
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.02.2013; Elsevier; Elsevier Limited
• Subjects: Algorithms; Biological and medical sciences; Brain - cytology; Colleges & universities; Computer Science; Diffusion MRI; Diffusion Tensor Imaging - methods; DTI estimation; Fundamental and applied biological sciences. Psychology; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Limited memory quasi-Newton method; Mean square errors; Medical Imaging; Methods; Nerve Fibers, Myelinated - ultrastructure; Noise; Non-local means; Pattern Recognition, Automated - methods; Reproducibility of Results; Sensitivity and Specificity; Total Kullback–Leibler divergence; Variational principle; Vertebrates: nervous system and sense organs; Diffusion MRI; Non-local means; DTI estimation; Total Kullback–Leibler divergence; Limited memory quasi-Newton method; Variational principle; Total Kullback―Leibler divergence; Memory; Nuclear magnetic resonance imaging; Total Kullback-Leibler divergence
• ISSN: 1053-8119; 1095-9572
• DOI: 10.1016/j.neuroimage.2012.11.012

Estimating diffusion tensors is an essential step in many applications — such as diffusion tensor image (DTI) registration, segmentation and fiber tractography. Most of the methods proposed in the literature for this task are not simultaneously statistically robust and feature preserving techniques. In this paper, we propose a novel and robust variational framework for simultaneous smoothing and estimation of diffusion tensors from diffusion MRI. Our variational principle makes use of a recently introduced total Kullback–Leibler (tKL) divergence for DTI regularization. tKL is a statistically robust dissimilarity measure for diffusion tensors, and regularization by using tKL ensures the symmetric positive definiteness of tensors automatically. Further, the regularization is weighted by a non-local factor adapted from the conventional non-local means filters. Finally, for the data fidelity, we use the nonlinear least-squares term derived from the Stejskal–Tanner model. We present experimental results depicting the positive performance of our method in comparison to competing methods on synthetic and real data examples. ► We use a statistically robust divergence-tBD for simultaneous smoothing and estimation of DTI. ► We use NLM as the weight for the regularization terms. This preserves the global structure. ► This method enables simultaneous denoising and DTI estimation.