F-boxes for filtering

Selecting a particular summative kernel (i.e., formally equivalent to a probability distribution) when filtering a digital signal can be a difficult task. An obvious solution to this problem is to filter with multiple kernels rather than with a single one, but the computing cost of such a solution can quickly become prohibitive (especially in real-time applications). Another alternative, the one studied in this paper, is to consider kernels modeled by imprecise probabilistic representations. Considering such representations makes the use of numerical tools coming from imprecise probability theory possible, such as the Choquet integral, and allows one to work with multiple kernels without multiplying too much the number of required computations. In this paper, we propose to use the well-known p-box representation to filter a digital signal. We show that the use p-boxes allows making more precise inferences than those obtained with possibility distributions and clouds. We then discuss the practical aspect of computing a filtered signal with pboxes, and finish by some experiments.