VDIP-TGV: Blind Image Deconvolution via Variational Deep Image Prior Empowered by Total Generalized Variation

Blind image deconvolution, the task of recovering a sharp image from a blurred observation with an unknown kernel, remains a challenging ill-posed inverse problem. While deep learning methods trained on large-scale datasets have achieved remarkable performance, their application is often limited by the availability of suitable training data. An alternative paradigm, zero-shot optimization methods like the Deep Image Prior (DIP), avoid this dependency but struggle with the inherent non-convexity of the blind deconvolution task. The Variational Deep Image Prior (VDIP) framework improves upon DIP by providing a more principled Bayesian formulation. However, its implicit regularization exhibits a strong first-order bias, akin to Total Variation, which tends to produce staircase artifacts in smooth regions and fails to adequately preserve fine-scale textures, especially when confronted with large blur kernels. To overcome this fundamental limitation, we propose VDIP-TGV, a novel method that integrates a second-order Total Generalized Variation (TGV) regularizer into the VDIP energy functional. The key insight is that the second-order nature of TGV penalizes inconsistencies in the image gradient field, promoting piecewise-affine solutions rather than just piecewise-constant ones. This allows our model to simultaneously preserve sharp edges and faithfully reconstruct smooth intensity transitions. We devise a robust optimization scheme based on the Alternating Direction Method of Multipliers (ADMM) that synergistically couples the implicit deep network prior with the explicit TGV regularizer, enabling stable joint estimation of both the image and the kernel. Extensive experiments demonstrate that VDIP-TGV achieves state-of-the-art results on challenging blind deblurring benchmarks. Notably, it shows significant advantages in robustness and fidelity over existing methods, particularly in scenarios involving severe blurs and complex image structures, validating the efficacy of our proposed second-order formulation.