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<p>We introduce a high-order total variation (TV) for sections of vector bundles over Riemannian manifolds, which is determined by the following geometric quadruplet: a connection and a positive definite metric on the vector bundle as well as a connection and a positive definite metric on the tangent bundle of the manifold. Then, we insert the high-order TV into the deep image prior (DIP), yielding a variational model for image restoration. The proposed model can be viewed as a combination of three classes of efficient variational models for image restoration: high-order TV-based models which promote the reconstruction of both edges and fine structures of the original image, geometric TV-based models which can encode extra properties of natural images, and DIP-based models which take benefit of the generative property of neural networks to reconstruct the original image. Experiments conducted up to the order 3 for image deblurring and super-resolution show that the higher the order, the better the results. Moreover, for a given order, the experiments also show that the proposed model outperforms its Euclidean restriction.</p>

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High-Order DIP-VBTV: An Image Restoration Model Combining a Deep Image Prior and a High-Order Total Variation on Vector Bundles

  • 期刊论文

  • 发表日期：

    2025年4月10日

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  • Thomas Batard

摘要

We introduce a high-order total variation (TV) for sections of vector bundles over Riemannian manifolds, which is determined by the following geometric quadruplet: a connection and a positive definite metric on the vector bundle as well as a connection and a positive definite metric on the tangent bundle of the manifold. Then, we insert the high-order TV into the deep image prior (DIP), yielding a variational model for image restoration. The proposed model can be viewed as a combination of three classes of efficient variational models for image restoration: high-order TV-based models which promote the reconstruction of both edges and fine structures of the original image, geometric TV-based models which can encode extra properties of natural images, and DIP-based models which take benefit of the generative property of neural networks to reconstruct the original image. Experiments conducted up to the order 3 for image deblurring and super-resolution show that the higher the order, the better the results. Moreover, for a given order, the experiments also show that the proposed model outperforms its Euclidean restriction.