Fractional Charlier moments for image reconstruction and image watermarking

Yamni, Mohamed; Daoui, Achraf; ogri, O. El; Karmouni, Hicham; Sayyouri, Mhamed; Qjidaa, Hassan; Flusser, Jan

doi:10.1016/j.sigpro.2020.107509

Cited by 80 publications

(26 citation statements)

References 43 publications

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“…We add experiments to compare the super-resolution part of our method with Fractional Charlier moments method [10] and Hahn moments method [11] using database Set14 and AVLetters [45]. The experiment result shows that the super-resolution part of our method has better performance in both visual effect and quantitative result.…”

Section: Othersmentioning

confidence: 97%

“…This article does not discuss interpolation-based methods and reconstructed-based methods since these two types of methods are usually treated as traditional methods. For example, moments-based methods are very popular in image reconstruction [8][9][10][11]. Example-based methods establish the relationship between LR and HR images to reconstruct the high-frequency part of the LR images.…”

Section: Introductionmentioning

confidence: 99%

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Optical Remote Sensing Image Denoising and Super-Resolution Reconstructing Using Optimized Generative Network in Wavelet Transform Domain

Feng

Zhang

et al. 2021

Remote Sensing

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High spatial quality (HQ) optical remote sensing images are very useful for target detection, target recognition and image classification. Due to the influence of imaging equipment accuracy and atmospheric environment, HQ images are difficult to acquire, while low spatial quality (LQ) remote sensing images are very easy to acquire. Hence, denoising and super-resolution (SR) reconstruction technology are the most important solutions to improve the quality of remote sensing images very effectively, which can lower the cost as much as possible. Most existing methods usually only employ denoising or SR technology to obtain HQ images. However, due to the complex structure and the large noise of remote sensing images, the quality of the remote sensing image obtained only by denoising method or SR method cannot meet the actual needs. To address these problems, a method of reconstructing HQ remote sensing images based on Generative Adversarial Network (GAN) named “Restoration Generative Adversarial Network with ResNet and DenseNet” (RRDGAN) is proposed, which can acquire better quality images by incorporating denoising and SR into a unified framework. The generative network is implemented by fusing Residual Neural Network (ResNet) and Dense Convolutional Network (DenseNet) in order to consider denoising and SR problems at the same time. Then, total variation (TV) regularization is used to furthermore enhance the edge details, and the idea of Relativistic GAN is explored to make the whole network converge better. Our RRDGAN is implemented in wavelet transform (WT) domain, since different frequency parts could be handled separately in the wavelet domain. The experimental results on three different remote sensing datasets shows the feasibility of our proposed method in acquiring remote sensing images.

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Section: Othersmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Optical Remote Sensing Image Denoising and Super-Resolution Reconstructing Using Optimized Generative Network in Wavelet Transform Domain

Feng

Zhang

et al. 2021

Remote Sensing

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“…The watermark extraction was done by applying PHFMs on watermarked images and the inverse of the embedding process in a blind extraction; this scheme is robust to different common geometric attacks. Yamni et al [ 20 ] suggested a digital watermark algorithm based on fractional Charlier moments (FCMs) and singular value decomposition (SVD). In this method, the host cover images are split into 8 × 8 blocks.…”

Section: Related Workmentioning

confidence: 99%

Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments

Abdel-Aziz

Hosny

Lashin

et al. 2021

Sensors

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This paper proposes a new blind, color image watermarking method using fast Walsh–Hadamard transformation (FWHT) and multi-channel fractional Legendre–Fourier moments (MFrLFMs). The input host color image is first split into 4 × 4 non-interfering blocks, and the MFrLFMs are computed for each block, where proper MFrLFMs coefficients are selected and FWHT is applied on the selected coefficients. The scrambled binary watermark has been inserted in the quantized selected MFrLFMs coefficients. The proposed method is a blind extraction, as the original host image is not required to extract the watermark. The proposed method is evaluated over many visual imperceptibility terms such as peak signal-to-noise ratio (PSNR), normalized correlation (NC), and bit error rate. The robustness of the proposed method is tested over several geometrical attacks such as scaling, rotation, cropping, and translation with different parameter values. The most widely recognized image processing attacks are also considered, e.g., compressing and adding noise attacks. A set of combination attacks are also tested to analyze the robustness of the proposed scheme versus several attacks. The proposed model’s experimental and numerical results for invisibility and robustness were superior to the results of similar watermarking methods.

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“…The discrete orthogonal moments (DOMs) are widely applied in various fields of signal and image analysis. Applications of DOMs include signal and image reconstruction [8,9,50], image classification [3,16,20,39], face recognition [33], image watermarking [24,41,44], signal zero-watermarking [10], edge detection [35], image encryption [43], signal compression [11,2] and image compression [13,42]. The computation of DOMs involves the computation of kernel discrete orthogonal polynomials (DOPs) such as Tchebichef [27,28], Krawtchouk [45,47], Hahn [46,50], Meixner [12,21], Charlier [8,19,34], dual Hahn [20,48], Racah [49] and Shmaliy [26] polynomials.…”

Section: Introductionmentioning

confidence: 99%

Fast and stable computation of higher-order Hahn polynomials and Hahn moment invariants for signal and image analysis

Daoui

Karmouni

Sayyouri

et al. 2021

Multimed Tools Appl

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This article presents, on the one hand, new algorithms for the fast and stable computation of discrete orthogonal Hahn polynomials of high order (HPs) based on the elimination of all gamma and factorial functions that cause the numerical fluctuations of HPs, and based on the use of appropriate stability conditions. On the other hand, a new method for the fast and numerically stable computation of Hahn moment invariants (HMIs) is also proposed. This method is mainly based on the use of new recursive relations of HPs and of matrix multiplications when calculating HMIs. To validate the efficiency of the algorithms proposed for the calculation of HPs, several signals and large images (≥4000 × 4000) are reconstructed by Hahn moments (HMs) up to the last order with a reconstruction error tending towards zero ( MSE ≃ 10 −10 ). The efficiency of the proposed method for calculating HMIs is demonstrated on large medical images (2048 × 2048) with a very low relative error ( RE ≃ 10 −10 ). Finally, comparisons with some recent work in the literature are provided.

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Fractional Charlier moments for image reconstruction and image watermarking

Cited by 80 publications

References 43 publications

Optical Remote Sensing Image Denoising and Super-Resolution Reconstructing Using Optimized Generative Network in Wavelet Transform Domain

Optical Remote Sensing Image Denoising and Super-Resolution Reconstructing Using Optimized Generative Network in Wavelet Transform Domain

Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments

Fast and stable computation of higher-order Hahn polynomials and Hahn moment invariants for signal and image analysis

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