Femtosecond spectroscopy is an important tool for tracking rapid photoinduced processes in a variety of materials. To spatially map the processes in a sample would substantially expand the capabilities of the method. This is, however, difficult to achieve due to the necessity to use low-noise detection and to maintain feasible data acquisition time. Here we demonstrate realization of an imaging pump-probe setup, featuring sub-100 fs temporal resolution, by a straightforward modification of a standard pump-probe technique, using a randomly structured probe beam. The structured beam, made by a diffuser, enabled us to computationally reconstruct the maps of transient absorption dynamics based on the concept of compressed sensing. We demonstrate the functionality of the setup in two proof-of-principle experiments, were we achieve spatial resolution of 20 μm. The presented concept provides a feasible route to imaging, using the pump-probe technique and ultrafast spectroscopy in general.