  We explore whether medium-resolution stellar spectra can be reconstructed
from photometric observations, taking advantage of the highly compressible
nature of the spectra. We formulate the spectral reconstruction as a
least-squares problem with a sparsity constraint. In our test case using data
from the Sloan Digital Sky Survey, only three broad-band filters are used as
input. We demonstrate that reconstruction using three principal components is
feasible with these filters, leading to differences with respect to the
original spectrum smaller than 5%. We analyze the effect of uncertainties in
the observed magnitudes and find that the available high photometric precision
induces very small errors in the reconstruction. This process may facilitate
the extraction of purely spectroscopic quantities, such as the overall
metallicity, for hundreds of millions of stars for which only photometric
information is available, using standard techniques applied to the
reconstructed spectra.
