  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 \mu m. The presented concept provides a
feasible route to imaging, using the pump-probe technique and ultrafast
spectroscopy in general.
