Circular Quasiconformal Deturbulence: Geometry-Based Restoration from Multiple Turbulent Frames

Imaging through inhomogeneous media often results in severe distortions, posing significant challenges to downstream image-processing tasks. The lack of clean paired images makes supervised learning impractical, motivating unsupervised restoration approaches. In this work, we propose the Circular Quasi-Conformal Deturbulence (CQCD) framework, an unsupervised approach that reconstructs distortion-free images from multiple frames using a circular architecture. The framework minimizes reconstruction errors by jointly estimating forward and backward transformations between distorted observations and the restored image. A key advancement of CQCD is the integration of computational quasi-conformal geometry, which encourages bijective non-rigid deformations and improves the well-posedness of both forward and inverse mappings for cycle consistency. The deformation field is further regularized to preserve structural coherence and reduce non-physical artifacts such as folding or tearing. Additionally, tight-frame blocks are employed to effectively encode distortion-sensitive features, enhancing the precision of the restoration process. To assess the effectiveness of the proposed framework, extensive evaluations are conducted on synthetic and real-world image datasets. Experimental findings indicate that CQCD not only surpasses existing state-of-the-art deturbulence techniques in restoration quality but also achieves highly accurate deformation field estimation.