Circular Quasiconformal Deturbulence: Geometry-Based Restoration from Multiple Turbulent Frames
Authors: Chu Chen, Han Zhang, Lok Ming Lui
Organizations: Department of Mathematics, City University of Hong Kong Hong Kong Centre for Cerebro-Cardiovascular Health Engineering Hong Kong · Department of Mathematics, Chinese University of Hong Kong Hong Kong
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.
Image restoration is fundamentally constrained by the tradeoff between distortion and perception: minimizing pixel-wise error yields over-smoothed results, whereas optimizing for perceptual realism often introduces structural deviations. Recent approaches attempt to balance this tradeoff via posterior sampling or multi-stage generative pipelines, yet remain computationally expensive and architecturally complex. To overcome these limitations, we propose PCFlow (Perceptually Consistent Flow Matching), a unified framework that directly parameterizes a continuous transport from degraded observations to clean targets, jointly optimizing distortion and perceptual quality. While its latent consistency flow objective drives stable and efficient few-step inference, a Latent Consistency Perceptual Loss (LCPL) imposes semantic constraints directly on the guiding velocity field, steering the dynamics toward visually sharp data manifolds. Furthermore, recognizing the inherent conflict between structural and perceptual consistencies, we integrate a conflict-free gradient projection strategy to stabilize the multi-objective optimization landscape. Combined with lightweight, convolution-only backbone, PCFlow achieves competitive performance across diverse restoration tasks at a fraction of traditional computational costs.
Single-frame atmospheric turbulence mitigation is inherently ill-posed due to spatially varying blur coupled with non-rigid geometric distortion. Existing end-to-end approaches trained on flat-field simulations often struggle to balance texture recovery with geometric rectification. To overcome this limitation, we propose D2Turb, a unified framework that bridges physics-grounded simulation with explicitly decoupled restoration. First, we introduce a Depth-Aware Turbulence Synthesis protocol that incorporates scene depth into the phase-to-space formulation. This generates physically consistent, depth-dependent degradations and provides a crucial intermediate tilt supervision signal for disentangled learning. Building upon this simulation engine, D2Turb decomposes restoration into two interactive stages: texture deblurring and geometric rectification. The texture deblurring stage employs a deblurring backbone to recover fine-grained details while preserving geometric distortion for the subsequent rectification stage. To mitigate the information fragmentation commonly observed in cascaded designs, we further propose an Adaptive Structural Prior Injection (ASPI) mechanism that dynamically transfers deep structural representations from the deblurring module to guide dense flow prediction for spatial unwarping. Extensive experiments demonstrate that D2Turb achieves state-of-the-art performance on both synthetic and real-world datasets, with consistent improvements in both texture recovery and geometric fidelity. Our code and pre-trained models are publicly available at https://github.com/HertzDot222/D2Turb.
All-in-one image restoration aims to recover clean images degraded by multiple corruption types using a single unified model. Existing methods typically rely on image-level prompts or shared guidance to handle diverse degradations. However, such a paradigm becomes inadequate when degradations are spatially heterogeneous or even coexist in mixed forms within a single image. Yet spatially adaptive guidance alone is not sufficient, since accurate restoration also requires each spatial query to reliably aggregate complementary information from local neighborhoods and global contexts. To this end, we propose QuReC, a unified framework for all-in-one image restoration. QuReC consists of a Degradation-Guided Query Reconstruction Module (DQRM) and a Local-Global Response Calibration Module (LGRCM). Specifically, DQRM matches each spatial query against a degradation prototype space to reconstruct a query-specific degradation-aware representation, thereby providing fine-grained spatially adaptive restoration guidance. To further stabilize this query-wise matching process, we introduce a weakly supervised prototype matching learning strategy to improve optimization stability and degradation semantic consistency. Meanwhile, LGRCM performs local-global dual-branch aggregation and calibrates the aggregated responses with learnable priors, improving the reliability of feature aggregation and the coordination between local detail modeling and global context modeling. Extensive experiments demonstrate that QuReC achieves superior performance on multiple all-in-one image restoration benchmarks. The code is released at https://github.com/zhoushen1/QuReC.