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

Fundamental Limits in Multimedia Forensics and Anti-forensics

As the use of multimedia editing tools increases, people become questioning the authenticity of multimedia content. This is specially a big concern for authorities, such as law enforcement, news reporter and government, who constantly use multimedia evidence to make critical decisions. To verify the authenticity of multimedia content, many forensic techniques have been proposed to identify the processing history of multimedia content under question. However, as new technologies emerge and more complicated scenarios are considered, the limitation of multimedia forensics has been gradually realized by forensic researchers. It is the inevitable trend in multimedia forensics to explore the fundamental limits. In this dissertation, we propose several theoretical frameworks to study the fundamental limits in various forensic problems. Specifically, we begin by developing empirical forensic techniques to deal with the limitation of existing techniques due to the emergence of new technology, compressive sensing. Then, we go one step further to explore the fundamental limit of forensic performance. Two types of forensic problems have been examined. In operation forensics, we propose an information theoretical framework and define forensicability as the maximum information features contain about hypotheses of processing histories. Based on this framework, we have found the maximum number of JPEG compressions one can detect. In order forensics, an information theoretical criterion is proposed to determine when we can and cannot detect the order of manipulation operations that have been applied on multimedia content. Additionally, we have examined the fundamental tradeoffs in multimedia antiforensics, where attacking techniques are developed by forgers to conceal manipulation fingerprints and confuse forensic investigations. In this field, we have defined concealability as the effectiveness of anti-forensics concealing manipulation fingerprints. Then, a tradeoff between concealability, rate and distortion is proposed and characterized for compression anti-forensics, which provides us valuable insights of how forgers may behave under their best strategy

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Wavelets and their use

This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous proofs of mathematical statements are omitted, and the reader is just referred to corresponding literature. The multiresolution analysis and fast wavelet transform became a standard procedure for dealing with discrete wavelets. The proper choice of a wavelet and use of nonstandard matrix multiplication are often crucial for achievement of a goal. Analysis of various functions with the help of wavelets allows to reveal fractal structures, singularities etc. Wavelet transform of operator expressions helps solve some equations. In practical applications one deals often with the discretized functions, and the problem of stability of wavelet transform and corresponding numerical algorithms becomes important. After discussing all these topics we turn to practical applications of the wavelet machinery. They are so numerous that we have to limit ourselves by some examples only. The authors would be grateful for any comments which improve this review paper and move us closer to the goal proclaimed in the first phrase of the abstract.Comment: 63 pages with 22 ps-figures, to be published in Physics-Uspekh

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Multimedia Protection using Content and Embedded Fingerprints

Improved digital connectivity has made the Internet an important medium for multimedia distribution and consumption in recent years. At the same time, this increased proliferation of multimedia has raised significant challenges in secure multimedia distribution and intellectual property protection. This dissertation examines two complementary aspects of the multimedia protection problem that utilize content fingerprints and embedded collusion-resistant fingerprints. The first aspect considered is the automated identification of multimedia using content fingerprints, which is emerging as an important tool for detecting copyright violations on user generated content websites. A content fingerprint is a compact identifier that captures robust and distinctive properties of multimedia content, which can be used for uniquely identifying the multimedia object. In this dissertation, we describe a modular framework for theoretical modeling and analysis of content fingerprinting techniques. Based on this framework, we analyze the impact of distortions in the features on the corresponding fingerprints and also consider the problem of designing a suitable quantizer for encoding the features in order to improve the identification accuracy. The interaction between the fingerprint designer and a malicious adversary seeking to evade detection is studied under a game-theoretic framework and optimal strategies for both parties are derived. We then focus on analyzing and understanding the matching process at the fingerprint level. Models for fingerprints with different types of correlations are developed and the identification accuracy under each model is examined. Through this analysis we obtain useful guidelines for designing practical systems and also uncover connections to other areas of research. A complementary problem considered in this dissertation concerns tracing the users responsible for unauthorized redistribution of multimedia. Collusion-resistant fingerprints, which are signals that uniquely identify the recipient, are proactively embedded in the multimedia before redistribution and can be used for identifying the malicious users. We study the problem of designing collusion resistant fingerprints for embedding in compressed multimedia. Our study indicates that directly adapting traditional fingerprinting techniques to this new setting of compressed multimedia results in low collusion resistance. To withstand attacks, we propose an anti-collusion dithering technique for embedding fingerprints that significantly improves the collusion resistance compared to traditional fingerprints