  The recent demonstration of isolated attosecond pulses from an X-ray
free-electron laser (XFEL) opens the possibility for probing ultrafast electron
dynamics at X-ray wavelengths. An established experimental method for probing
ultrafast dynamics is X-ray transient absorption spectroscopy, where the X-ray
absorption spectrum is measured by scanning the central photon energy and
recording the resultant photoproducts. The spectral bandwidth inherent to
attosecond pulses is wide compared to the resonant features typically probed,
which generally precludes the application of this technique in the attosecond
regime. In this paper we propose and demonstrate a new technique to conduct
transient absorption spectroscopy with broad bandwidth attosecond pulses with
the aid of ghost imaging, recovering sub-bandwidth resolution in
photoproduct-based absorption measurements.
