# Restoration of Atmospheric Turbulence-distorted Images via RPCA and Quasiconformal Maps

## TL;DR

This paper introduces a novel method combining RPCA and quasiconformal maps to effectively restore high-quality images from sequences distorted by atmospheric turbulence, addressing both geometric distortion and spatial-temporal blur.

## Contribution

The proposed algorithm uniquely integrates RPCA and quasiconformal maps for turbulence distortion correction, providing a new approach to image restoration in challenging atmospheric conditions.

## Key findings

- Effective reduction of geometric distortion and blur.
- Restoration of image details and improved visual quality.
- Validated on synthetic and real turbulence-distorted videos.

## Abstract

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.