Section: New Results

Multi-dimensional differentiation

Participants : Samer Riachy, Mamadou Mboup, Jean-Pierre Richard.

Multivariate signals are involved in all branches of physics. To name a few, they can be in digital images and videos, telecommunication, geology, archeology and econometrics. Estimating partial derivatives of multi-dimensional signals is an old ill-posed problem. Using multivariate Taylor series expansion, multivariate Laplace transform and adequate algebraic manipulations we obtain very efficient partial derivatives estimators [97] , [96] , [98] . In fact those estimators correspond to orthogonal projection in a Jacobi basis i.e., a least squares minimization. In addition they can be implemented as finite impulse digital filters. We combine somehow optimization and fast computation. Applications in image processing namely motion detection are in progress.