BGGMM-HMT based locally optimum image watermark detector in high-order NSST difference domain

Imperceptibility, robustness and data payload are three main requirements of any image watermarking systems to guarantee desired functionalities, but there is a tradeoff among them from the information-theoretic perspective. How to achieve this balance is a major challenge. In this paper, we propose a new statistical image watermarking scheme, which is based on the high-order difference coefficients in nonsubsampled Shearlet transform (NSST) domain and the bounded generalized Gaussian mixture model-based hidden Markov tree (BGGMM-HMT). In the watermark embedding process, we use a nonlinear embedding approach to hide the digital watermark into the robust high-order difference coefficients, which can achieve better imperceptibility. In the watermark detection process, high-order difference coefficients are accurately modeled by using BGGMM-HMT, where the distribution characteristics of high-order difference coefficients can be captured through BGGMM, and the scale dependencies of high-order difference coefficients can be captured through HMT. Statistical model parameters are then estimated by combining the approach of minimizing the higher bound on data negative log-likelihood function and upward–downward algorithm. Finally, an image watermark detector based on BGGMM-HMT is developed using the locally optimum (LO) decision rule. For the proposed detector, the receiver operating characteristic (ROC) expression is derived in detail. We evaluate the proposed scheme from different aspects and compare it with the state-of-the-art schemes. After a large number of experimental tests, the encouraging results obtained prove the effectiveness of our watermarking scheme.     

Bayesian Wavelet-Based Image Denoising Using the Gauss–Hermite Expansion

The probability density functions (PDFs) of the wavelet coefficients play a key role in many wavelet-based image processing algorithms, such as denoising. The conventional PDFs usually have a limited number of parameters that are calculated from the first few moments only. Consequently, such PDFs cannot be made to fit very well with the empirical PDF of the wavelet coefficients of an image. As a result, the shrinkage function utilizing any of these density functions provides a substandard denoising performance. In order for the probabilistic model of the image wavelet coefficients to be able to incorporate an appropriate number of parameters that are dependent on the higher order moments, a PDF using a series expansion in terms of the Hermite polynomials that are orthogonal with respect to the standard Gaussian weight function, is introduced. A modification in the series function is introduced so that only a finite number of terms can be used to model the image wavelet coefficients, ensuring at the same time the resulting PDF to be non-negative. It is shown that the proposed PDF matches the empirical one better than some of the standard ones, such as the generalized Gaussian or Bessel K-form PDF. A Bayesian image denoising technique is then proposed, wherein the new PDF is exploited to statistically model the subband as well as the local neighboring image wavelet coefficients. Experimental results on several test images demonstrate that the proposed denoising method, both in the subband-adaptive and locally adaptive conditions, provides a performance better than that of most of the methods that use PDFs with limited number of parameters.      

Bayesian wavelet-based image denoising using the gauss-hermite expansion

The probability density functions (PDFs) of the wavelet coefficients play a key role in many wavelet-based image processing algorithms, such as denoising. The conventional PDFs usually have a limited number of parameters that are calculated from the first few moments only. Consequently, such PDFs cannot be made to fit very well with the empirical PDF of the wavelet coefficients of an image. As a result, the shrinkage function utilizing any of these density functions provides a substandard denoising performance. In order for the probabilistic model of the image wavelet coefficients to be able to incorporate an appropriate number of parameters that are dependent on the higher order moments, a PDF using a series expansion in terms of the Hermite polynomials that are orthogonal with respect to the standard Gaussian weight function, is introduced. A modification in the series function is introduced so that only a finite number of terms can be used to model the image wavelet coefficients, ensuring at the same time the resulting PDF to be non-negative. It is shown that the proposed PDF matches the empirical one better than some of the standard ones, such as the generalized Gaussian or Bessel K-form PDF. A Bayesian image denoising technique is then proposed, wherein the new PDF is exploited to statistically model the subband as well as the local neighboring image wavelet coefficients. Experimental results on several test images demonstrate that the proposed denoising method, both in the subband-adaptive and locally adaptive conditions, provides a performance better than that of most of the methods that use PDFs with limited number of parameters.     

一种文本图像水印的算法研究

该文提出了一种文本图像水印的新算法。首先将文本中选定嵌入水印的区域视为一个彩色图像,对其进行离散余弦变换（DCT）,并将变换系数进行加密排序之后,则经典的乘性水印算法转变为加性算法。将排序之后的DCT系数视为分叉噪声,而水印信号为弱信号,那么利用加性噪声中弱信号榆测理论推导出一种水印检测器来检测水印信号,并对其检测性能进行了理论和实验分析。实验表明这种检测器对于高斯加性噪声、中值滤波、乘性噪音以及低通滤波等多种攻击手段都具有较好的抗攻击能力。     

Design and statistical analysis of a hash-aided image watermarking system

This paper develops a joint hashing/watermarking scheme in which a short hash of the host signal is available to a detector. Potential applications include content tracking on public networks and forensic identification. The host data into which the watermark is embedded are selected from a secret subset of the full-frame discrete cosine transform of an image, and the watermark is inserted through multiplicative embedding. The hash is a binary version of selected original image coefficients. We propose a maximum likelihood watermark detector based on a statistical image model. The availability of a hash as side information to the detector modifies the posterior distribution of the marked coefficients. We derive Chernoff bounds on the receiver operating characteristic performance of the detector. We show that host-signal interference can be rejected if the hash function is suitably designed. The relative difficulty of an eavesdropper's detection problem is also determined; the eavesdropper does not know the secret key used. Monte Carlo simulations are performed using photographic test images. Finally, various attacks on the watermarked image are introduced to study the robustness of the derived detectors. The joint hashing/watermarking scheme outperforms the traditional "hashless" watermarking technique.     

The zero-rate spread-spectrum watermarking game

This paper develops a game-theoretic methodology to design and embed M messages in signals and images in the presence of an adversary. Here, M is assumed to be subexponential in the signal's sample size (zero-rate transmission), and the embedding is done using spread-spectrum watermarking. The detector performs statistical hypothesis testing. The system is designed to minimize probability of error under the worst-case attack in a prescribed class of attacks. The variables in this game are probability distributions for the watermarker and attacker. Analytical solutions are derived under the assumption of Gaussian host vectors, watermarks and attacks, and squared-error distortion constraints for the watermarker and the attacker. The Karhunen-Loeve transform (KLT) plays a central role in this study. The optimal distributions for the watermarker and the attacker are Gaussian test channels applied to the KLT coefficients; the game is then reduced to a maxmin power-allocation problem between the channels. As a byproduct of this analysis, we can determine the optimal tradeoff between using the most efficient (in terms of detection performance) signal components for transmission and spreading the transmission across many components (to fool the attacker's attempts to eliminate the watermark). We also conclude that in this framework, additive watermarks are suboptimal; they are, however, nearly optimal in a small-distortion regime. The theory is applied to watermarking of autoregressive processes and to wavelet-based image watermarking. The optimal watermark design outperforms conventional designs based on heuristic power allocations and/or simple correlation detectors.     

Decision feedback differential phase detection of M-ary DPSKsignals

Multiple-symbol differential phase detection (DFDPD) based on decision feedback of past detected symbols is presented for M-ary DPSK modulation. Adopting a Gaussian phase noise assumption, we obtain the a posteriori joint probability density function (PDF) of the outputs of L DPD defectors of orders of 1 to L symbols and derive a DF-DPD algorithm which is based on feeding back the L-1 past detected symbols and minimizing the sum of phase errors of L DPD detectors. A practical implementation of the DF-DPD receiver is presented that uses a single conventional (one-symbol) DPD detector. The bit error rate (BER) performance in an additive white Gaussian noise (AWGN) channel is analyzed taking into account decision error propagation. Performance improvements are evaluated by computer simulations in AWGN and Rayleigh fading channels     

Spread spectrum watermark detection in DRT-domain

The traditional correlation-based detector is optimal only for Gaussian data, but the Laplacian Probability Density Function (PDF) is more appropriate to model the coefficients in the Discrete Ridgelet Transform (DRT) domain. An additive maximum-likelihood detector based on the Laplacian PDF is analyzed and the theoretical result of its performance is given. The experiments show that the error of the Laplacian model for the DRT coefficients of many images is smaller than that of the Gaussian model. The experiments also prove that the Laplacian detector is superior to the tradi- tional correlation-based detector.     

Simulation Results for the Decision-Directed MAP Receiver for M-ary Signals in Mulitiplicative and Additive Gaussian Noise

Simulation results are presented for the error-rate performance of the recursive digital maximum a posteriori probability (MAP) detector for knownM-ary signals in multiplicative and additive Gaussian noise. The structure of the digital simulation of the optimum detector is generally described, with specific results obtained for a quaternary signal and 2500 digit per second transmission rate. The simulation is focused on the aeronautical multipath communication problem. Plots of detection error rate versus additive signal-to-noise ratio are given, with the power ratio of multiplicative process to desired signal as a parameter. Results are presented for the cases where the detector has perfect knowledge of the first- and second-order statistics of the multiplicative and additive processes and also where these statistics are estimated in near real time. For comparison, the error rates of conventional coherent and noncoherent digital MAP detectors are also obtained. It is shown that with nonzero multiplicative noise, the error rates of the conventional detectors saturate at a level that is irreducible for increasing additive signal-to-noise ratio. The error rate of the optimum detector having perfect statistical knowledge continues to decrease rapidly with increasing additive signal-to-noise ratio. In the absence of multiplicative noise, the conventional coherent detector and the optimum detector are shown to exhibit identical performance. Suboptimum detectors, having less than perfect statistical knowledge, yield error rates bounded below by the optimum detector rates and bounded above by the conventional detector rates.     

基于变分贝叶斯学习的音频水印盲检测方法

为了提高音频水印的检测性能,基于音频帧MFCC特征的统计特性,提出了一种音频水印盲检测方法。在音频帧的DCT系数上嵌入扩频水印,对嵌入水印的音频帧和原始音频帧分别提取MFCC特征进行训练,分别建立高斯混合模型,并通过变分贝叶斯学习方法估计出高斯混合模型的参数,检测时依据最大似然的原则。实验结果显示提出的方法在音频信号受到噪声干扰和恶意攻击的情况下,相对基于EM算法的方法在误检率上有明显降低,在小样本训练情况下具有更好的效果并且可以有效避免过拟合的问题。     

非高斯杂波下知识辅助检测的认知方法

先验信息的使用是提高雷达目标检测性能的有效途径之一,然而先验信息与当前探测环境的失配会严重影响到检测器的性能.本文考虑逆伽马分布纹理、复合高斯杂波下的知识辅助检测算法,推导了先验模型失配条件下(逆伽马分布参数失配)检测器的虚警率和Swerling I型目标的检测概率计算公式,获得了检测性能与模型参数失配之间的量化关系.利用两组不同参数的知识辅助检测器对当前杂波环境进行探测,通过评估检测器的性能,实现了当前杂波环境模型参数的估计.计算机仿真和实测数据的分析结果表明,采用认知方法的知识辅助检测器较常规检测器而言,能够获得更好的检测性能.     

Statistics of 2-D DT-CWT Coefficients for a Gaussian Distributed Signal

This paper deals with the statistical properties of the two-dimensional dual-tree complex wavelet transform (DT-CWT) coefficients of a Gaussian distributed signal both in the Cartesian and polar forms. The first level of decomposition of the DT-CWT uses the wavelet filters that form only an approximate Hilbert-pair, while those at the higher levels form almost an exact Hilbert-pair. Hence, a significant correlation exists between the quadrature-filtered coefficients of the two trees in the first level of decomposition as compared to the other levels. As a consequence, in the Cartesian representation, the real and imaginary components of the complex coefficients are modeled as independent zero-mean Gaussian having unequal variances for the first level of decomposition and equal variances for the higher levels. In the polar representation, the magnitude components are modeled by a generalized Gamma probability density function (PDF) for the first-level decomposition and a Rayleigh PDF for the higher levels. The corresponding phase components are modeled by an analytic PDF. The Monte Carlo simulations show that the proposed PDFs of the transform coefficients match very well with the empirical ones. It is shown that the moments of the corresponding PDFs closely approximate the estimated sample moments. Finally, two techniques, namely, maximum a posteriori-based estimation and phase-based ridge detection are developed using the proposed PDFs. Simulation studies are carried out showing that the use of the proposed techniques provides improved estimation and detection performance of images in a noisy environment.      

基于双通道检测的多比特盲水印最优检测器的设计

水印检测错误会严重损害水印系统的可信度。该文提出基于双谱和能量检测的双通道检测来实现最优盲水印检测器的设计,并给出了一种在小波域中的具体实现。传统检测方法检测概率会随着信噪比的下降而急剧下降。双通道检测时信噪比很小时只要有足够大的双谱信息,即可得到较高的检测概率。即使双谱信息很小时双通道检测系统退化为似然比检测系统,仍是最优的。检测器检测到指定的水印后利用独立分量分析技术进行水印盲恢复。实验过程中攻击由通用水印测试软件Stirmark产生,实验数据证明所设计的最优盲检测器对Stirmark提供的各种攻击(如剪切、JPEG压缩、删行/列、旋转、尺度变换、随机几何攻击等)具有很好的鲁棒性。实验结果说明这种最优检测器的性能优越于现有的水印检测器。     

Asymptotically optimal detection for additive watermarking in the DCT and DWT domains

Most of the watermarking schemes that have been proposed until now employ a correlation detector (matched filter). The current paper proposes a new detector scheme that can be applied in the case of additive watermarking in the DCT (discrete cosine transform) or DWT (discrete wavelet transform) domain. Certain properties of the probability density function of the coefficients in these domains are exploited. Thus, an asymptotically optimal detector is constructed based on well known results of the detection theory. Experimental results prove the superiority of the proposed detector over the correlation detector.     

Image watermarking using DNST-PHFMs magnitude domain vector AGGM-HMT

Invisibility, robustness and payload are three indispensable and contradictory properties for any image watermarking systems. Therefore, in this paper a novel statistical image watermark decoder based on robust discrete nonseparable Shearlet transform (DNST)-polar harmonic Fourier moments (PHFMs) magnitude and effective vector anisotropic generalized Gaussian mixtures (AGGM)-hidden Markov tree (HMT). We begin with a detailed study on the robustness and statistical characteristics of local DNST- PHFMs magnitudes of natural images. This study reveals the excellent robustness, highly non-Gaussian marginal statistics and strong dependencies of local DNST-PHFMs magnitudes. We also find that conditioned on their generalized neighborhoods, the local DNST-PHFMs magnitudes can be approximately modeled as anisotropic generalized Gaussian variables. Based on these findings, we model local DNST-PHFMs magnitudes using a vector AGGM-HMT that can capture all interscale, interdirection, and interlocation dependencies. Meanwhile, model parameters can be estimated effectively by using localization clues guided expectation–maximization (LCGEM) approach. Finally, we develop a new statistical image watermark decoder using the vector AGGM-HMT and maximum likelihood (ML) decision rule. Extensive experimental results show the superiority of the proposed watermark decoder over several state-of-the-art statistical watermarking methods and some approaches based on convolutional neural networks.     

Autocorrelation-Based Decentralized Sequential Detection of OFDM Signals in Cognitive Radios

This paper introduces a simple and computationally efficient spectrum sensing scheme for Orthogonal Frequency Division Multiplexing (OFDM) based primary user signal using its autocorrelation coefficient. Further, it is shown that the log likelihood ratio test (LLRT) statistic is the maximum likelihood estimate of the autocorrelation coefficient in the low signal-to-noise ratio (SNR) regime. Performance of the local detector is studied for the additive white Gaussian noise (AWGN) and multipath channels using theoretical analysis. Obtained results are verified in simulation. The performance of the local detector in the face of shadowing is studied by simulations. A sequential detection (SD) scheme where many secondary users cooperate to detect the same primary user is proposed. User cooperation provides diversity gains as well as facilitates using simpler local detectors. The sequential detection reduces the delay and the amount of data needed in identification of the underutilized spectrum. The decision statistics from individual detectors are combined at the fusion center (FC). The statistical properties of the decision statistics are established. The performance of the scheme is studied through theory and validated by simulations. A comparison of the SD scheme with the Neyman-Pearson fixed sample size (FSS) test for the same false alarm and missed detection probabilities is also carried out.     

DCT域图像水印的局部优化检测性能研究

水印检测是数字水印技术最关键的步骤之一.水印检测的传统方法是采用线性相关的方法,但是该方法存在问题.本文根据数字图像离散余弦变换(DCT)域交流系数的广义高斯分布模型,对图像水印的局部优化检测方法进行了推导,并给出了水印检测器检测性能的理论分析结果.实验结果验证了图像水印局部优化检测方法检测性能理论分析的有效性,以及实际检测性能的优越性.     

Robust image watermarking based on multiband wavelets and empirical mode decomposition.

In this paper, we propose a blind image watermarking algorithm based on the multiband wavelet transformation and the empirical mode decomposition. Unlike the watermark algorithms based on the traditional two-band wavelet transform, where the watermark bits are embedded directly on the wavelet coefficients, in the proposed scheme, we embed the watermark bits in the mean trend of some middle-frequency subimages in the wavelet domain. We further select appropriate dilation factor and filters in the multiband wavelet transform to achieve better performance in terms of perceptually invisibility and the robustness of the watermark. The experimental results show that the proposed blind watermarking scheme is robust against JPEG compression, Gaussian noise, salt and pepper noise, median filtering, and ConvFilter attacks. The comparison analysis demonstrate that our scheme has better performance than the watermarking schemes reported recently.     

饱和检测器在数字水印方案中的应用

本文利用饱和检测器在离散余弦变换(DCT)域水印方案中进行水印检测.饱和检测器无须事先了解原始图像和水印,实现盲水印检测.在加入噪声、滤波以及压缩图片中进行水印检测,体现出了算法的鲁棒性.