<title>Separable and radial bases for medical image processing</title>

Abstract

The goal of this paper is to describe a consistent method which permits to define discrete image processing operators in the same way as discrete image formation operators. This is done via the use of the generalized sampling theorem which establishes the relationship between continuous and discrete functions according to the mean-square error in a spline or bandlimited subspace. A discrete operator is defined according to its continuous counterpart operating on continuous functions in the same subspace. Classical medical image acquisition bases often are radial where classical image processing operators are deduced from separable bases. The paper shows the trends between these two imperatives for medical image processing, explains where are the risks for information loss induced by implementing discrete linear operators and presents two methods to partially or totally keep the initial stored information.