Possibilistic signal processing: How to handle noise?

We propose a novel approach for noise quantifier at each location of a signal. This method is based on replacing the conventional kernel-based approach extensively used in signal processing by an approach involving another kind of kernel: a possibility distribution. Such an approach leads to interval-valued resulting methods instead of point-valued ones. We propose a theoretical justification to this approach and we show, on real and artificial data sets, that the length of the obtained interval and the local noise level are highly correlated. This method is non-parametric and has an advantage over other methods since no assumption about the nature of the noise has to be made, except its local ergodicity. Besides, the propagation of the noise in the involved signal processing method is direct and does not require any additional computation.