A two-level method for image denoising and image deblurring models using mean curvature regularization

Fairag, Faisal; Chen, Ke; Brito‐Loeza, Carlos; Ahmad, Shahbaz

doi:10.1080/00207160.2021.1929939

Cited by 7 publications

(2 citation statements)

References 21 publications

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“…High order geometric TVs involving Riemannian geometry mainly rely on the Gaussian or mean curvature of the image graph (see e.g. [21], [22], [23], [24]). Experiments conducted on different image restoration tasks show an improvement with respect to the original TVbased model [2].…”

Section: Geometric Tv Modelsmentioning

confidence: 99%

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

Batard

2024

Preprint

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We introduce a high order Total Variation (TV) for sections of vector bundles over Riemannian manifolds, and 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 the restoration of grey-level and color images. 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 promotes 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 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.

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Section: Geometric Tv Modelsmentioning

confidence: 99%

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

Batard

2024

Preprint

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“…This regularization method has been less popular compared to the more general image regularization models due to the complexity in solving the MC mathematical model which comprises of higher order derivatives. Faisal Fairag et al (4) propose a two-level method to solve this problem where the mathematical model is split into two steps, the first step forms a nonlinear system including the higher order derivatives and the second step is a large problem with low order derivatives. The authors show that this MC regularization model results in effective image deblurring.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Sparsity through Hybrid Regularization for Effective Image Deblurring

S¹,

Mallikarjunaswamy²,

Sharmila³

2021

IJST

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Objectives: To develop image deblurring algorithm to effectively recover the original image from the captured blurry and noisy image. Methods: A novel image deblurring algorithm using adaptive priors is proposed. The adaptive priors vary the sparsity induced based on factors such as the type of blur affecting the image, image region, statistical parameters regarding the blur kernel and/or statistical predictions on the blur kernel. The proposed algorithm using adaptive priors improves the quality of the deblurred result, when compared with various recent image deblurring algorithms. Finding: the work contains a case study with regard to certain standard parameters. It is observed that proposed method is better in terms of frequency response, Peak signal-tonoise ratio (PSNR) and Structural Similarity Index (SSIM) values in comparison with other priors. Novelty: the proposed priors lead to the most effective results for image deblurring using the Bayesian framework. The proposed method improves the performance by 30% in PSNR and 45% in SSIM values in dB with uniform kernel size 12 * 12 and improves performance by 30 % in PSNR and 32% SSIM with a standard deviation of 3.5. The proposed method enhances the frequency response of the real-time image restoration process. Applications: Some important applications include the restoration of medical images such as MRI images, CT images where the intensity of these radiations is maintained to avoid damage to human organs. Remote sensing images captured through drones at a specified time cannot be retaken and hence restoring such images is very important. Similarly restoring images from CCTV footage, astronomical images.

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