PDE-based efficient method for colour image restoration

Bettahar, S.; Lambert, Patrick; Stambouli, A. Boudghène

doi:10.1016/j.camwa.2017.05.011

Cited by 5 publications

(1 citation statement)

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“…I MAGE denoising is an important issue in information processing field. In the last decade, many popular methods, including partial differential equation (PDE) based methods [1]- [3], dictionary learning [4], [5], sparse representation [5]- [7] and non-negative matrix factorization based methods [8] etc., emerge in these fields such as signal and image processing, medical, seismic and remote sensing imaging and compressed sensing. In this paper, we mainly focus on the PDE-based image denoising methods.…”

Section: Introductionmentioning

confidence: 99%

A Spatially Adaptive Edge-Preserving Denoising Method Based on Fractional-Order Variational PDEs

Wang

Nieto

et al. 2020

IEEE Access

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Image denoising is a basic problem in image processing. An important task of image denoising is to preserve the significant geometric features such as edges and textures while filtering out noise. So far, this is still a problem to be further studied. In this paper, we firstly introduce an edge detection function based on the Gaussian filtering operator and then analyze the filtering characteristic of the fractional derivative operator. On the basis, we establish the spatially adaptive fractional edge-preserving denoising model in the variational framework, discuss the existence and uniqueness of our proposed model solution and derive the nonlinear fractional Euler-Lagrange equation for solving our proposed model. This forms a fractional order extension of the first and second order variational approaches. Finally, we apply the proposed method to the synthetic images and real seismic data denoising to verify the effectiveness of our method and compare the experimental results of our method with the related state-of-the-art methods. Experimental results illustrate that our proposed method can not only improve the signal to noise ratio (SNR) but also adaptively preserve the structural information of an image compared with other contrastive methods. Our proposed method can also be applied to remote sensing imaging, medical imaging and so on.

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