Phase-diversity techniques provide a novel observational method for ov
ercoming the effects of turbulence and instrument-induced aberrations
in ground-based astronomy. Two implementations of phase-diversity tech
niques that differ with regard to noise model, estimator, optimization
algorithm, method of regularization, and treatment of edge effects ar
e described. Reconstructions of solar granulation derived by applying
these two implementations to common data sets are shown to yield nearl
y identical images. For both implementations, reconstructions from pha
se-diverse speckle data (involving multiple realizations of turbulence
) are shown to be superior to those derived from conventional phase-di
versity data (involving a single realization). Phase-diverse speckle r
econstructions are shown to achieve near diffraction-limited resolutio
n and are validated by internal and external consistency tests, includ
ing a comparison with a reconstruction using a well-accepted speckle-i
maging method.