An interval-valued inversion of the non-additive interval-valued F-transform: Use for upsampling a signal

Abstract

As shown in a recent paper, the fuzzy transform can be reinterpreted as a sampling process with an ill-known sampling kernel (or point spread function). This reinterpretation leads to an interval-valued direct fuzzy transform: the non-additive fuzzy transform. It provides the convex set of all sampled values that should have been obtained by sampling a continuous signal with a convex set of sampling kernels. Its dual transform, the non-additive inverse fuzzy transform, allows computation of an interval-valued reconstruction of a sampled signal, which is the set of all values that would have been obtained by interpolating or approximating this sampled signal when using a convex set of reconstruction kernels. In this paper, we consider using a new interval-valued inversion process within this new framework to upsample a signal, i.e. reconstruct a high resolution signal with a low resolution signal, in a semi-blind context. As illustrated in the experimental part of the paper, the main advantage of using this method, compared to previous techniques, is its inherent robustness with respect to modeling the sampling process.