Stable computation of higher order Charlier moments for signal and image reconstruction

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

doi:10.1016/j.ins.2020.02.019

Cited by 54 publications

(34 citation statements)

References 37 publications

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“…Experiment 2. Considering the serious effect of noise on image reconstruction [ 35 ], the trend of change in reconstruction errors with the increase in order was tested when different values of

were taken after the same salt and pepper noises were added. Thirty images were used for this experiment, the mean value of reconstruction errors was taken for the 30 images,

was set to varying number within the range from 10 to 100,

, and salt and pepper noises at intensity levels of 0.05, 0.1, 0.15, and 0.2 were added, respectively.…”

Section: Experiments and Analysis Of Experimental Resultsmentioning

confidence: 99%

Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Wang

Gao

Yang

et al. 2021

Sensors

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Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

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“…Experiment 2. Considering the serious effect of noise on image reconstruction [ 35 ], the trend of change in reconstruction errors with the increase in order was tested when different values of

were taken after the same salt and pepper noises were added. Thirty images were used for this experiment, the mean value of reconstruction errors was taken for the 30 images,

was set to varying number within the range from 10 to 100,

, and salt and pepper noises at intensity levels of 0.05, 0.1, 0.15, and 0.2 were added, respectively.…”

Section: Experiments and Analysis Of Experimental Resultsmentioning

confidence: 99%

Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Wang

Gao

Yang

et al. 2021

Sensors

View full text Add to dashboard Cite

show abstract

“…Since the noise would seriously affect the reconstruction performance of images [39], this experiment tested the comparison of the image reconstruction errors between GFrEMs, TFrEMs, GFrPHFMs, GFrRHFMs, GFrPCETs, GFrPCTs, and GFrPSTs after adding the salt and pepper noise. is experiment used the average value of thirty images.…”

Section: Methodsmentioning

confidence: 99%

Accurate Computation of Fractional-Order Exponential Moments

Hao

et al. 2020

Security and Communication Networks

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Exponential moments (EMs) are important radial orthogonal moments, which have good image description ability and have less information redundancy compared with other orthogonal moments. Therefore, it has been used in various fields of image processing in recent years. However, EMs can only take integer order, which limits their reconstruction and antinoising attack performances. The promotion of fractional-order exponential moments (FrEMs) effectively alleviates the numerical instability problem of EMs; however, the numerical integration errors generated by the traditional calculation methods of FrEMs still affect the accuracy of FrEMs. Therefore, the Gaussian numerical integration (GNI) is used in this paper to propose an accurate calculation method of FrEMs, which effectively alleviates the numerical integration error. Extensive experiments are carried out in this paper to prove that the GNI method can significantly improve the performance of FrEMs in many aspects.

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“…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%

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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Stable computation of higher order Charlier moments for signal and image reconstruction

Cited by 54 publications

References 37 publications

Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Accurate Computation of Fractional-Order Exponential Moments

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

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