  Turbulence-degraded image frames are distorted by both turbulent deformations
and space-time-varying blurs. To suppress these effects, we propose a
multi-frame reconstruction scheme to recover a latent image from the observed
image sequence. Recent approaches are commonly based on registering each frame
to a reference image, by which geometric turbulent deformations can be
estimated and a sharp image can be restored. A major challenge is that a fine
reference image is usually unavailable, as every turbulence-degraded frame is
distorted. A high-quality reference image is crucial for the accurate
estimation of geometric deformations and fusion of frames. Besides, it is
unlikely that all frames from the image sequence are useful, and thus frame
selection is necessary and highly beneficial. In this work, we propose a
variational model for joint subsampling of frames and extraction of a clear
image. A fine image and a suitable choice of subsample are simultaneously
obtained by iteratively reducing an energy functional. The energy consists of a
fidelity term measuring the discrepancy between the extracted image and the
subsampled frames, as well as regularization terms on the extracted image and
the subsample. Different choices of fidelity and regularization terms are
explored. By carefully selecting suitable frames and extracting the image, the
quality of the reconstructed image can be significantly improved. Extensive
experiments have been carried out, which demonstrate the efficacy of our
proposed model. In addition, the extracted subsamples and images can be put in
existing algorithms to produce improved results.
