  Images collected with ground-based telescopes suffer blurring and distortions
from turbulence in Earth's atmosphere. Adaptive optics (AO) can only partially
compensate for these effects. Neither multi-frame blind deconvolution (MFBD)
nor speckle techniques restore AO-compensated images to the correct power
spectrum and contrast. MFBD can only compensate for a finite number of
low-order aberrations, leaving a tail of uncorrected high-order modes. Speckle
restoration of AO-corrected data depends on calibrations of the AO corrections
and assumptions regarding the height distribution of atmospheric turbulence. We
seek to develop an improvement to MFBD that combines speckle's usage of
turbulence statistics to account for high-order modes with the ability of MFBD
to sense low-order modes that can be partially corrected by AO and/or include
fixed or slowly changing instrumental aberrations. We modify the
image-formation model, supplementing the fitted low-order wavefront aberrations
with tails of random high-order aberrations. These tails follow Kolmogorov
statistics scaled to estimated or measured values of Fried's parameter, r0,
that characterize the strength of the seeing at the moment of data collection.
We refer to this as statistical diversity (SD). We test MFBD with SD with
noise-free synthetic data, simulating many different r0 and numbers of
AO-corrected modes. SD improves the contrasts and power spectra of restored
images, both in accuracy and in consistency with varying r0, without penalty in
processing time. With focus diversity (FD), the results are almost perfect. SD
also reduces errors in the fitted wavefront parameters. MFBD with SD and FD
seems resistant to several percents of error in r0. Adding SD to MFBD shows
great promise for improving contrasts and power spectra in restored images.
Further studies with real data are merited.
