Femtosecond spectroscopy is an important tool used for tracking rapid photoinduced processes in a variety of materials. To spatially map the processes in a sample would substantially expand the method's capabilities. This is, however, difficult to achieve, due to the necessity of using low-noise detection and maintaining feasible data acquisition time. Here, we demonstrate realization of an imaging pump-probe setup, featuring sub-100 fs temporal resolution, by using a straightforward modification of a standard pump-probe technique, which uses 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 setup's functionality in two proof-of-principle experiments, where we achieve spatial resolution of 20 μm. The presented concept provides a feasible route to imaging, by using the pump-probe technique and ultrafast spectroscopy in general.