  Ultrafast spectroscopy is an important tool for studying photoinduced
dynamical processes in atoms, molecules, and nanostructures. Typically, the
time to perform these experiments ranges from several minutes to hours
depending on the choice of spectroscopic method. It is desirable to reduce this
time overhead to not only to shorten time and laboratory resources, but also to
make it possible to examine fragile specimens which quickly degrade during long
experiments. In this article, we motivate using compressive sensing to
significantly shorten data acquisition time by reducing the total number of
measurements in ultrafast spectroscopy. We apply this technique to experimental
data from ultrafast transient absorption spectroscopy and ultrafast terahertz
spectroscopy and show that good estimates can be obtained with as low as 15% of
the total measurements, implying a 6-fold reduction in data acquisition time.
