  Light passing through scattering media will be strongly scattered and
diffused into complex speckle pattern, which contains almost all the spatial
information and spectral information of the objects. Although various methods
have been proposed to recover the spatial information of the hidden objects, it
is still a challenge to simultaneously obtain their spectral information. Here,
we present an effective approach to realize spectral imaging through scattering
media by combining the spectra retrieval and the speckle-correlation. Compared
to the traditional imaging spectrometer, our approach is more flexible in the
choice of core element. In this paper, we have demonstrated employing the
frosted glass as the core element to achieve spectral imaging. Obtaining the
spectral information and spatial information are demonstrated via numerical
simulations. Experiment results further demonstrate the performance of our
scheme in spectral imaging through scattering media. The spectral imaging based
on scattering media is well suited for new type spectral imaging applications.
