Tropical Graph Signal Processing

For the past few years, the domain of graph signal processing has extended classical Fourier analysis to domains described by graphs. Most of the results were obtained by analogy with the study of heat propagation. We propose to perform a similar analysis in the context of tropical algebra, widely used in theoretical computer science to monitor propagation processes over graphs of distances. We introduce a Tropical Graph Fourier Transform and prove a few results on graph inference and the existence of a tropical uncertainty principle.