N dimensional Mojette transform. Application to multiple description

The Mojette transform allows to exactly represent a discrete signal from a finite set of hyper-planes. This generic transform (many projection directions, choice of the number of projections, spline order) always ensures a very low complexity comparable to the FFT. In this paper, the Mojette transform in dimension n is presented and results issued from 2D and 3D cases are generalized. The central slice theorem, used with the Radon transform, is also derived in dimension n. Two schemes of applicatives examples enlight the interest for this generalization in the domain of multiple description.