Contourlet Domain Image Modeling and its Applications in Watermarking and Denoising

Statistical image modeling in sparse domain has recently attracted a great deal of research interest. Contourlet transform as a two-dimensional transform with multiscale and multi-directional properties is known to effectively capture the smooth contours and geometrical structures in images. The objective of this thesis is to study the statistical properties of the contourlet coefficients of images and develop statistically-based image denoising and watermarking schemes. Through an experimental investigation, it is first established that the distributions of the contourlet subband coefficients of natural images are significantly non-Gaussian with heavy-tails and they can be best described by the heavy-tailed statistical distributions, such as the alpha-stable family of distributions. It is shown that the univariate members of this family are capable of accurately fitting the marginal distributions of the empirical data and that the bivariate members can accurately characterize the inter-scale dependencies of the contourlet coefficients of an image. Based on the modeling results, a new method in image denoising in the contourlet domain is proposed. The Bayesian maximum a posteriori and minimum mean absolute error estimators are developed to determine the noise-free contourlet coefficients of grayscale and color images. Extensive experiments are conducted using a wide variety of images from a number of databases to evaluate the performance of the proposed image denoising scheme and to compare it with that of other existing schemes. It is shown that the proposed denoising scheme based on the alpha-stable distributions outperforms these other methods in terms of the peak signal-to-noise ratio and mean structural similarity index, as well as in terms of visual quality of the denoised images. The alpha-stable model is also used in developing new multiplicative watermark schemes for grayscale and color images. Closed-form expressions are derived for the log-likelihood-based multiplicative watermark detection algorithm for grayscale images using the univariate and bivariate Cauchy members of the alpha-stable family. A multiplicative multichannel watermark detector is also designed for color images using the multivariate Cauchy distribution. Simulation results demonstrate not only the effectiveness of the proposed image watermarking schemes in terms of the invisibility of the watermark, but also the superiority of the watermark detectors in providing detection rates higher than that of the state-of-the-art schemes even for the watermarked images undergone various kinds of attacks

Probabilistic modeling of wavelet coefficients for processing of image and video signals

Statistical estimation and detection techniques are widely used in signal processing including wavelet-based image and video processing. The probability density function (PDF) of the wavelet coefficients of image and video signals plays a key role in the development of techniques for such a processing. Due to the fixed number of parameters, the conventional PDFs for the estimators and detectors usually ignore higher-order moments. Consequently, estimators and detectors designed using such PDFs do not provide a satisfactory performance. This thesis is concerned with first developing a probabilistic model that is capable of incorporating an appropriate number of parameters that depend on higher-order moments of the wavelet coefficients. This model is then used as the prior to propose certain estimation and detection techniques for denoising and watermarking of image and video signals. Towards developing the probabilistic model, the Gauss-Hermite series expansion is chosen, since the wavelet coefficients have non-compact support and their empirical density function shows a resemblance to the standard Gaussian function. A modification is introduced in the series expansion so that only a finite number of terms can be used for modeling the wavelet coefficients with rendering the resulting PDF to become negative. The parameters of the resulting PDF, called the modified Gauss-Hermite (NIGH) PDF, are evaluated in terms of the higher-order sample-moments. It is shown that the MGH PDF fits the empirical density function better than the existing PDFs that use a limited number of parameters do. The proposed MGH PDF is used as the prior of image and video signals in designing maximum a posteriori and minimum mean squared error-based estimators for denoising of image and video signals and log-likelihood ratio-based detector for watermarking of image signals. The performance of the estimation and detection techniques are then evaluated in terms of the commonly used metrics. It is shown through extensive experimentations that the estimation and detection techniques developed utilizing the proposed MGH PDF perform substantially better than those that utilize the conventional PDFs. These results confirm that the superior fit of the MGH PDF to the empirical density function resulting from the flexibility of the MGH PDF in choosing the number of parameters, which are functions of higher-order moments of data, leads to the better performance. Thus, the proposed MGH PDF should play a significant role in wavelet-based image and video signal processin

Proceedings of the 19th Sound and Music Computing Conference

Proceedings of the 19th Sound and Music Computing Conference - June 5-12, 2022 - Saint-Étienne (France). https://smc22.grame.f