Hamidreza Sadreazami

A Study of Multiplicative Watermark Detection in the Contourlet Domain Using Alpha-Stable Distributions

In the past decade, several schemes for digital image watermarking have been proposed to protect the copyright of an image document or to provide proof of ownership in some identifiable fashion. This paper proposes a novel multiplicative watermarking scheme in the contourlet domain. The effectiveness of a watermark detector depends highly on the modeling of the transform-domain coefficients. In view of this, we first investigate the modeling of the contourlet coefficients by the alpha-stable distributions. It is shown that the univariate alphastable distribution fits the empirical data more accurately than the formerly used distributions, such as the generalized Gaussian and Laplacian, do. We also show that the bivariate alpha-stable distribution can capture the across scale dependencies of the contourlet coefficients. Motivated by the modeling results, a blind watermark detector in the contourlet domain is designed by using the univariate and bivariate alpha-stable distributions. It is shown that the detectors based on both of these distributions provide higher detection rates than that based on the generalized Gaussian distribution does. However, a watermark detector designed based on the alpha-stable distribution with a value of its parameter α other than 1 or 2 is computationally expensive because of the lack of a closed-form expression for the distribution in this case. Therefore, a watermark detector is designed based on the bivariate Cauchy member of the alpha-stable family for which α = 1. The resulting design yields a significantly reduced-complexity detector and provides a performance that is much superior to that of the GG detector and very close to that of the detector corresponding to the best-fit alpha-stable distribution. The robustness of the proposed bivariate Cauchy detector against various kinds of attacks, such as noise, filtering, and compression, is studied and shown to be superior to that of the generalized Gaussian detector.

Multiplicative Watermark Decoder in Contourlet Domain Using the Normal Inverse Gaussian Distribution

In recent years, many works on digital image watermarking have been proposed all aiming at protection of the copyright of an image document or authentication of data. This paper proposes a novel watermark decoder in the contourlet domain . It is known that the contourlet coefficients of an image are highly non-Gaussian and a proper distribution to model the statistics of the contourlet coefficients is a heavy-tailed PDF. It has been shown in the literature that the normal inverse Gaussian (NIG) distribution can suitably fit the empirical distribution. In view of this, statistical methods for watermark extraction are proposed by exploiting the NIG as a prior for the contourlet coefficients of images. The proposed watermark extraction approach is developed using the maximum likelihood method based on the NIG distribution. Closed-form expressions are obtained for extracting the watermark bits in both clean and noisy environments. Experiments are performed to verify the robustness of the proposed decoder. The results show that the proposed decoder is superior to other decoders in terms of providing a lower bit error rate. It is also shown that the proposed decoder is highly robust against various kinds of attacks such as noise, rotation, cropping, filtering, and compression.

Contourlet domain image modeling by using the alpha-stable family of distributions

It is known that the contourlet coefficients of images have non-Gaussian property and heavy tails. In view of this, an appropriate distribution to model the statistics of the contourlet coefficients would be the one having large peaks, and tails heavier than that of a Gaussian PDF, i.e., a heavy-tailed PDF. This paper proposes a new image modeling in the contourlet domain, where the magnitudes of the coefficients are modeled by a symmetric alpha-stable distribution which is best suited for modeling transform coefficients with a high non-Gaussian property and heavy tails. It is shown that the alpha-stable family of distributions provides a more accurate model to the contourlet subband coefficients than the formerly used distributions, namely, the generalized Gaussian and Laplacian distributions, both in terms of the subjective measure of the Kolmogorov-Smirnov distance and the objective measure of comparing the log-scale histograms.

Contourlet domain image denoising using normal inverse gaussian distribution

A new contourlet-based method is introduced for reducing noise in images corrupted by additive white Gaussian noise. It is shown that a symmetric normal inverse Gaussian distribution is more suitable for modeling the contourlet coefficients than formerly-used generalized Gaussian distribution. To estimate the noise-free coefficients, a Bayesian maximum a posteriori estimator is developed utilizing the proposed distribution. In order to estimate the parameters of the distribution, a moment-based technique is used. The performance of the proposed method is studied using typical noise-free images corrupted with simulated noise and compared with that of the other state-of-the-art methods. It is shown that compared with other denoising techniques, the proposed method gives higher values of the peak signal-to-noise ratio and provides images of good visual quality.

A study on image denoising in contourlet domain using the alpha-stable family of distributions

In the past decade, several image denoising techniques have been developed aiming at recovering signals from noisy data as much as possible along with preserving the features of an image. This paper proposes a new image denoising method in the contourlet domain by using the alpha-stable family of distributions as a prior for contourlet image coefficients. The univariate symmetric alpha-stable distribution (SαS) is mostly suited for modeling of the i.i.d. contourlet coefficients with high non-Gaussian property and heavy tails. In addition, the bivariate SαS exploits the dependencies between the coefficients across scales. In this paper, using the univariate and bivariate priors, Bayesian minimum mean absolute error and maximum a posteriori estimators are developed in order to estimate the noise-free contourlet coefficients. To estimate the parameters of the alpha-stable distribution, a spatially-adaptive method using fractional lower order moments is proposed. It is shown that the proposed parameter estimation method is superior to the maximum likelihood method. An extension to color image denoising is also developed. Experiments are carried out using noise-free images corrupted by additive Gaussian noise, and the results show that the proposed denoising method outperforms other existing methods in terms of the peak signal-to-noise ratio and mean structural similarity index, as well as in visual quality of the denoised images. HighlightsA study on alpha-stable distribution of contourlet transform for image denoising.Development of Bayesian MMAE and MAP estimators for image denoising applications.Development of a new parameter estimation method for alpha-stable distribution.Denoising of color images using the correlation of the RGB channels.A comparative study of proposed denoising method and methods using other models.

A Robust Multiplicative Watermark Detector for Color Images in Sparse Domain

In recent years, digital watermarking has facilitated the protection of copyright information through embedding hidden information into the digital content. In this brief, for the first time, a blind multichannel multiplicative color image watermarking scheme in the sparse domain is proposed. In order to take into account the cross correlation between the coefficients of the color bands in the sparse domain, a statistical model based on the multivariate Cauchy distribution is used. The statistical model is then used to derive an efficient closed-form decision rule for the watermark detector. Experimental results and theoretical analysis are presented to validate the proposed watermark detector. The performance of the proposed detector is compared with that of the other detectors. The results demonstrate the improved detection rate and high robustness against the commonly used attacks such as JPEG compression, salt and pepper noise, median filtering, and Gaussian noise.

Analysis of dispersion characteristic of substrate integrated waveguide based on mode matching method

In this paper, β-ω of substrate integrated waveguide is studied. First, a unit cell of the whole structure is analyzed by mode matching technique. Then by applying Floquet theory into the solution process, dispersion characteristic of the periodic structure is obtained and effects of various parameters of the structure on the response are described. Finally, proposed method is validated by comparing our results with other published results and Ansofts HFSS.

Analysis of substrate integrated waveguide based on two dimensional multi-port method

In this article, two-dimensional analysis is proposed to calculate propagation constant of substrate integrated waveguide. First, the impedance matrix of a unit cell structure of substrate integrated waveguide is calculated by employing desegmentation method. Then, propagation constant of fundamental mode is obtained by applying Floquet theorem on the impedance matrix of the unit cell. Field distribution of the propagating mode is also acquired. Our results show good agreement with published results. Comparison with results obtained by high-frequency structure simulator validates this method for a broad range of dimensions.

Optimum multiplicative watermark detector in contourlet domain using the normal inverse Gaussian distribution

Digital watermarking has been widely used in the copyright protected images in multimedia. This paper addresses the blind watermark detection problem in contourlet domain. It is known that the contourlet coefficients of images have non-Gaussian property and can be well modelled by non-Gaussian distributions such as the normal inverse Gaussian (NIG). In view of this, we exploit this model to derive closed-form expressions for the test statistics and design an optimum blind watermark detector in the contourlet domain. Through conducting several experiments, the performance of the proposed detector is evaluated in terms of the probabilities of detection and false alarm and compared to that of the other existing detectors. It is shown that the proposed detector using the NIG distribution is superior to other detectors in terms of providing higher rate of detection. It is also shown that the proposed NIG-based detector is more robust than other detectors against attacks, such as JPEG compression and Gaussian noise.

Image denoising utilizing the scale-dependency in the contourlet domain

A new contourlet-based method is introduced for reducing noise in images corrupted by additive white Gaussian noise. This method takes into account the statistical dependencies among the contourlet coefficients of different scales. In view of this, a non-Gaussian multivariate distribution is proposed to capture the across-scale dependencies of the contourlet coefficients. This model is then exploited in a Bayesian maximum a posteriori estimator to restore the clean coefficients by deriving an efficient closed-form shrinkage function. Experimental results are performed to evaluate the performance of the proposed denoising method using typical noise-free images contaminated by simulated noise. The results show that the proposed method outperforms some of the state-of-the-art methods in terms of both the subjective and objective criteria.