Dynamic compressive response of rigid closed-cell polymeric foams under high strain rate direct impact loading conditions is investigated. The foam specimens are subjected to direct impact loading, while their deformation response is observed and quantified using high speed photography in conjunction with 3D digital image correlation. A modified single stage shock tube apparatus with an aluminum projectile are used to generate the direct impact loading. The load applied on the specimen is measured using the load-cells at the other end of the specimen. The major challenge in high strain experiments, i.e. achieving equilibrium at the early stages of the deformation, has been compensated by performing an inverse analysis and accounting for the effect of inertia stresses into the analysis. The full-field acceleration distribution has first been calculated over the entire regions of interest. Then the inertia stresses are determined considering a one-dimensional equation of motion, and superimposed to the stress magnitude measured from the load-cells. The effects of material compressibility and the local change of density have also been included in the analysis. For this purpose, a mathematical model based on the principle of conservation of mass is proposed which enables the calculation of the local material density as a function of initial density, local plastic strain and local plastic Poisson's ratio. Finally, the dynamic stress-strain responses of the foam specimens are presented as a function of foam density. The failure mechanisms as a function of foam density and loading rate are discussed.