  Pulsar scintillation allows a glimpse into small-scale plasma structures in
the interstellar medium, if we can infer their properties from the
scintillation pattern. With Very Long Baseline Interferometry and working in
delay-delay rate space, where the contributions of pairs of images to the
interference pattern become localized, the scattering geometry and distribution
of scattered images on the sky can be determined if a single,
highly-anisotropic scattering screen is responsible for the scintillation.
However, many pulsars are subject to much more complex scattering environments
where this method cannot be used. We present a novel technique to reconstruct
the scattered flux of the pulsar and solve for the scattering geometry in these
cases by combining interferometric visibilities with cross-correlations of
single-station intensities. This takes advantage of the fact that, considering
a single image pair in delay-delay rate space, the visibilities are sensitive
to the sum of the image angular displacements, while the cross-correlated
intensities are sensitive to the difference, so that their combination can be
used to localize both images of the pair. We show that this technique is able
to reconstruct the published scattering geometry of PSR B0834+06, then apply it
to simulations of more complicated scattering systems, where we find that it
can distinguish features from different scattering screens even when the
presence of multiple screens is not obvious in the Fourier transform of the
dynamic spectrum. This technique will allow us to both better understand the
distribution of scattering within the interstellar medium and to apply current
scintillometry techniques, such as modelling scintillation and constraining the
location of pulsar emission, to sources for which a current lack of
understanding of the scattering environment precludes the use of these
techniques. (abridged)
