A lot of methods and models in classical digital signal processing applications assume that all probabilities are precise, that is, that there exists some complete probabilistic information about the system and component behavior. The completeness of the probabilistic information is in agreement with the classical approach which consists in modeling the sensor acquisition procedure by the convolution of the real physical signal with a unique summative kernel. The completeness of the probabilistic information is a naive assumption. We soften this assumption by considering the possibility theory instead of the probability theory to manage the uncertain components and particularly to model the signal acquistion procedure. Indeed possibility theory is more appropriate to deal with incompleteness of the probabilistic information.

A maxitive kernel is a weighted neighborhood of a given location, formally similar to a possibility distribution or membership function of a normalized fuzzy subset. We chose this model because of its simplicity. Indeed the fact that we can represent this imprecise model by a function, a possibility distribution, is a huge advantage for computation purposes. Most of the imprecise models can not be uniquely determined by such a function. Another advantage of using maxitive kernels is that the operations needed in the digital signal processing applications with summative kernels can be easily adapted to maxitive kernels.