Filtering with clouds
Résumé
Selecting a particular kernel to filter a given digital signal can be a difficult task. One solution to solve this difficulty is to filter with multiple kernels. However, this solution can be computationally costly. Using the fact that most kernels used for low-pass signal filtering can be assimilated to probability distributions (or linear combinations of probability distributions), we propose to model sets of kernels by convex sets of probabilities. In particular, we use specific representations that allow us to perform a robustness analysis without added computational costs. The result of this analysis is an interval-valued filtered signal. Among such representations are possibility distributions, from which have been defined maxitive kernels. However, one drawback of maxitive kernels is their limited expressiveness. In this paper, we extend this approach by considering another representation of convex sets of probabilities, namely clouds, from which we define cloudy kernels. We show that cloudy kernels are able to represent sets of kernels whose bandwidth is upper and lower bounded, and can therefore be used as a good trade-off between the classical and the maxitive approach, avoiding some of their respective shortcomings without making computations prohibitive. Finally, the benefits of using cloudy filters is demonstrated through some experiments.
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