  We propose a practical strategy for choosing sets of input coherent states
that are near-optimal for reconstructing single-mode Gaussian quantum processes
with output-state heterodyne measurements. We first derive analytical
expressions for the mean squared-error that quantifies the reconstruction
accuracy for general process tomography and large data. Using such expressions,
upon relaxing the trace-preserving constraint, we introduce an error-reducing
set of input coherent states that is independent of the measurement data or the
unknown true process -- the geometrical set. We numerically show that process
reconstruction from such input coherent states is nearly as accurate as that
from the best possible set of coherent states chosen with the complete
knowledge about the process. This allows us to efficiently characterize
Gaussian processes even with reasonably low-energy coherent states. We
numerically observe that the geometrical strategy without trace preservation
beats all nonadaptive strategies for arbitrary trace-preserving Gaussian
processes of typical parameter ranges so long as the displacement components
are not too large.
