A new generation of experiments is expected to shed light on the elusive parton structure of the bound proton. One of the most promising directions is incoherent deeply virtual Compton scattering, which can provide a tomographic view of the bound proton. The first measurement has been recently performed, using 4 He targets at Jefferson Lab. In the work presented here, a rigorous Impulse Approximation analysis of this process is proposed. As ingredients, state-of-theart models of the nuclear spectral function and of the parton structure of the struck proton, together with novel scattering amplitudes expressions for a bound moving nucleon, have been used. A good overall agreement with the data is obtained, in particular at high values of the photon virtuality. The observed big difference between results for the bound proton and those for the free one turns out to be due in small part to modifications of the parton structure, and rather it should be related to kinematical nuclear effects. The analysis demonstrates that the comparison of the results of this approach, based on a conventional description, with future precise data, has the potential to expose exotic quark and gluon effects in nuclei.