We address the problem of restoring a high-quality image from an observed image sequence strongly distorted by atmospheric turbulence. A novel algorithm is proposed in this paper to reduce geometric distortion as well as space-and-time-varying blur due to strong turbulence. By considering a suitable energy functional, our algorithm first obtains a sharp reference image and a subsampled image sequence containing sharp and mildly distorted image frames with respect to the reference image. The subsampled image sequence is then stabilized by applying the Robust Principal Component Analysis (RPCA) on the deformation fields between image frames and warping the image frames by a quasiconformal map associated with the low-rank part of the deformation matrix. After image frames are registered to the reference image, the low-rank part of them are deblurred via a blind deconvolution, and the deblurred frames are then fused with the enhanced sparse part. Experiments have been carried out on both synthetic and real turbulence-distorted video. Results demonstrate that our method is effective in alleviating distortions and blur, restoring image details and enhancing visual quality.

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Turbulence-degraded image frames are distorted by both turbulent deformations and space-timevarying 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.

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