The measurements performed in Japan have shown that muon radiography is an “imaging technique” capable of providing information of the internal structure of volcanoes with a resolution and richness of details beyond the reach of conventional, non-imaging techniques. The measurements have been performed using electronic detectors or nuclear emulsions. The latter have shown excellent muon tracking capabilities and space resolution, but are lacking of the capability of electronic detectors to provide data in real time. In this paper, we examine the possibility of developing an electronic detector giving a resolution comparable to that of nuclear emulsions and with a larger area than used so far, in order to see deeper structures inside volcanoes in spite of the strong muon absorption in the rock. We specifically discuss the very challenging application of muon radiography to Mt. Vesuvius, driven by the strong social interest coming from the enormous potential danger which it represents. Applications to other volcanoes can be envisaged.