  In this paper, we consider black holes in the consistent Aoki-Gorji-Mukohyama
theory of the four-dimensional Einstein-Gauss-Bonnet (4D EGB) gravity in the
presence of Born-Infeld (BI) nonlinear electrodynamics. We study several
optical features of these black holes such as the shadow radius, energy
emission rate and deflection angle, and analyse the effect of the coupling
constants, the electric charge and cosmological constant on the considered
optical quantities. Furthermore, we also employ the connection between the
shadow radius and quasinormal modes (QNMs) and investigate small scalar
perturbations around the black hole solution. We show that the variation of the
parameters of the theory provide specific signatures on the optical features of
the BI charged black hole solution, thus leading to the possibility of directly
testing this consistent Aoki-Gorji-Mukohyama 4D EGB black hole model by using
astrophysical observations.
