A convex semi-definite positive framework for DTI estimation and regularization

Authors:
Radhouène Neji;Noura Azzabou;Nikos Paragios;Gilles Fleury
Affiliations:
Laboratoire des Mathématiques Appliquées aux Systèmes, Ecole Centrale Paris, Châtenay-Malabry, France and Département Signaux et Systèmes Electroniques, Ecole Sup ...;Laboratoire des Mathématiques Appliquées aux Systèmes, Ecole Centrale Paris, Châtenay-Malabry, France;Laboratoire des Mathématiques Appliquées aux Systèmes, Ecole Centrale Paris, Châtenay-Malabry, France;Département Signaux et Systèmes Electroniques, Ecole Supérieure d'Electricité, Gif-sur-Yvette, France
Venue:
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part I
Year:
2007

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Abstract

In this paper we introduce a novel variational method for joint estimation and regularization of diffusion tensor fields from noisy raw data. To this end, we use the classic quadratic data fidelity term derived from the Stejskal-Tanner equation with a new smoothness term leading to a convex objective function. The regularization term is based on the assumption that the signal can be reconstructed using a weighted average of observations on a local neighborhood. The weights measure the similarity between tensors and are computed directly from the diffusion images. We preserve the positive semi-definiteness constraint using a projected gradient descent. Experimental validation and comparisons with a similar method using synthetic data with known noise model, as well as classification of tensors towards understanding the anatomy of human skeletal muscle demonstrate the potential of our method.