We develop a method of quantum state imaging (determination of the full initial density matrix of an atomic or molecular state) using time dependent spectrum data. The method determines the wave function (or more generally, the density matrix) created via an arbitrary excitation process even when degenerate rotational degrees of freedom are present. It requires application of external electric and magnetic fields, without which determination of the full density matrix is in general impossible. In the presence of external fields, quantum state imaging from angle and polarization resolved (or unresolved) time dependent spectrum data is feasible.