title: BHATTACHARYYA MEDIAN OF SYMMETRIC POSITIVE-DEFINITE MATRICES AND APPLICATION TO THE DENOISING OF DIFFUSION-TENSOR FIELDS.
abstract: In this paper, we present algorithms for the computation of the median of a set of symmetric positive-definite matrices using different distances/divergences. The novelty of this paper lies in the median computation using the Bhattacharya distance on diffusion tensors. The numerical computation of the median is achieved using the gradient descent algorithm and the fixed point algorithm. We present an application namely, one of denoising tensor-valued data using median filters constructed using several distance/divergences and compare their performance.
authors.affiliation: Tunisia Polytechnic School, University of Carthage, B.P. 743, 2078 La Marsa, Tunisia ; Dept. of CISE, University of Florida, Gainesville, Florida 32611.
authors.forename: Malek
authors.initials: M
authors.lastname: Charfi
authors.affiliation: LAMSIN, ENIT, University of Tunis El Manar, B.P. 37, 1002 Tunis-Belvédèere, Tunisia.
authors.forename: Zeineb
authors.initials: Z
authors.lastname: Chebbi
authors.affiliation: LAMSIN, ENIT, University of Tunis El Manar, B.P. 37, 1002 Tunis-Belvédèere, Tunisia.
authors.forename: Maher
authors.initials: M
authors.lastname: Moakher
authors.affiliation: Dept. of CISE, University of Florida, Gainesville, Florida 32611.
authors.forename: Baba C
authors.initials: BC
authors.lastname: Vemuri
keywords: Bhattacharyya median; Log-Euclidean median; Riemannian median