The formation and evolution of deformation bands in a carbonate rock with high porosity is investigated by performing in situ triaxial experiments with high-resolution synchrotron X-Ray Computed Tomography by placing a specifically designed testing device directly in the tomograph. The processing of images by Digital Volume Correlation techniques provides insight on the deformation modes of the samples for various loading conditions. In more porous specimens with a homogeneous microstructure, many subhorizontal compactant deformation bands sequentially initiate, propagate, widen and fully saturate the volume of the rock sample after a few percent of overall strain, leading to a rather uniform compaction of the sample. In contrast, denser samples with a more heterogeneous microstructure exhibit discrete deformation bands, in limited number. These bands propagate and widen, leading to strong localization of the deformation which remains restricted to certain parts of the sample.