  In recent years, group equivariant non-expansive operators (GENEOs) have
attracted attention in the fields of Topological Data Analysis and Machine
Learning. In this paper we show how these operators can be of use also for the
removal of impulsive noise and to increase the stability of TDA in the presence
of noisy data. In particular, we prove that GENEOs can control the expected
value of the perturbation of persistence diagrams caused by uniformly
distributed impulsive noise, when data are represented by $L$-Lipschitz
functions from $\mathbb{R}$ to $\mathbb{R}$.
