  The computation of real-time properties, such as transport coefficients or
bound state spectra of strongly interacting quantum fields in thermal
equilibrium is a pressing matter. Since the sign problem prevents a direct
evaluation of these quantities, lattice data needs to be analytically continued
from the Euclidean domain of the simulation to Minkowski time, in general an
ill-posed inverse problem. Here we report on a novel approach to improve the
determination of real-time information in the form of spectral functions by
setting up a simulation prescription in imaginary frequencies. By carefully
distinguishing between initial conditions and quantum dynamics one obtains
access to correlation functions also outside the conventional Matsubara
frequencies. In particular the range between $\omega_0$ and $\omega_1=2\pi T$,
which is most relevant for the inverse problem may be more highly resolved. In
combination with the fact that in imaginary frequencies the kernel of the
inverse problem is not an exponential but only a rational function we observe
significant improvements in the reconstruction of spectral functions,
demonstrated in a simple 0+1 dimensional scalar field theory toy model.
