We report the results of a simulation, using diffuse laser light and an optical bench, of our recent holographic interpretation of Labeyrie's speckle interferometry. Our approach applies to a wide class of multiple objects (such as close binary, or higher order, stars) viewed through a turbulent medium (such as the atmosphere, under all ‘seeing’ conditions). Our results should encourage astronomers to attempt to image those multiple star systems whose individual components would be resolvable in large telescopes were there no atmosphere to contend with, but whose details are always, or usually, obscured by atmospheric seeing. We find that we can get clear images of collections of small, isolated objects after processing only 20 speckle interferograms (we must emphasize, though, that the signal to noise ratio is high in our experiments i.e. each interferogram contains several hundred speckles). We find that our reconstructions of large, continuous objects are recognizable, although appreciably distorted. We attribute this to the virtual unavoidable non-linearities introduced by our processing methods, which are entirely optical and photographic. We suggest that improved results would be obtained by a suitable combination of optical and digital processing procedures. We point out that our results support those who hope to improve the performance of inferior optical instruments by using processing methods inspired by statistical concepts.