In digital watermarking schemes, imperceptibility, robustness, and capacity are three fundamental yet conflicting performance metrics. Recent advancements in statistical model-based approaches have attracted growing attention due to their potential to balance these competing requirements. Existing methods are limited in their ability to simultaneously ensure sufficient capacity while enhancing both robustness and imperceptibility. To address this limitation, we propose a hybrid domain statistical image watermarking (HDSIW) scheme by leveraging vector finite Student's-t mixture (FSM) based hidden Markov tree (HMT) modeling of non-subsampled Shearlet transform (NSST) domain fast generic polar complex exponential transform (FGPCET) magnitudes. The NSST-FGPCET magnitudes are offered as a novel watermark embedding domain. A novel edge-based adaptive embedding localization method is proposed. The vector FSM-HMT is constructed using the marginal statistical features and dependencies of the NSST-FGPCET magnitudes. The decoder is derived based on the maximum likelihood criterion and the vector FSM-HMT. In addition, we propose a metric to effectively measure the balance between imperceptibility and robustness. Extensive experiments have shown that the proposed HDSIW outperforms state-of-the-art methods in terms of imperceptibility and robustness. The HDSIW can accommodate sufficient watermark capacity with favorable imperceptibility and robustness.

Sparse superposition (SS) codes provide an efficient communication scheme over the Gaussian channel, utilizing the vector approximate message passing (VAMP) decoder for rotational invariant design matrices [1]. Previous work has established that the VAMP decoder for SS achieves Shannon capacity when the design matrix satisfies a specific spectral criterion and exponential decay power allocation is used [2]. In this work, we propose a spatially coupled VAMP (SC-VAMP) decoder for SS with spatially coupled design matrices. Based on state evolution (SE) analysis, we demonstrate that the SC-VAMP decoder is capacity-achieving when the design matrices satisfy the spectra criterion. Empirically, we show that the SC-VAMP decoder outperforms the VAMP decoder with exponential decay power allocation, achieving a lower section error rate. All codes are available on https://github.com/yztfu/SC-VAMP-for-Superposition-Code.git.

We investigate the performance of a Bayesian statistician tasked with recovering a rank-k signal matrix SS⊤∈ ℝn×n, corrupted by element-wise additive Gaussian noise. This problem lies at the core of numerous applications in machine learning, signal processing, and statistics. We derive an analytic expression for the asymptotic mean-square error (MSE) of the Bayesian estimator under mismatches in the assumed signal rank, signal power, and signal-to-noise ratio (SNR), considering both sphere and Gaussian signals. Additionally, we conduct a rigorous analysis of how rank mismatch influences the asymptotic MSE. Our primary technical tools include the spectrum of Gaussian orthogonal ensembles (GOE) with low-rank perturbations and asymptotic behavior of k-dimensional spherical integrals.

The integration of artificial intelligence (AI) and mobile networks is regarded as one of the most important scenarios for 6G. In 6G, a major objective is to realize the efficient transmission of task-relevant data. Then a key problem arises, how to design collaborative AI models for the device side and the network side, so that the transmitted data between the device and the network is efficient enough, which means the transmission overhead is low but the AI task result is accurate. In this paper, we propose the multi-link information bottleneck (ML-IB) scheme for such collaborative models design. We formulate our problem based on a novel performance metric, which can evaluate both task accuracy and transmission overhead. Then we introduce a quantizer that is adjustable in the quantization bit depth, amplitudes, and breakpoints. Given the infeasibility of calculating our proposed metric on high-dimensional data, we establish a variational upper bound for this metric. However, due to the incorporation of quantization, the closed form of the variational upper bound remains uncomputable. Hence, we employ the Log-Sum Inequality to derive an approximation and provide a theoretical guarantee. Based on this, we devise the quantized multi-link information bottleneck (QML-IB) algorithm for collaborative AI models generation. Finally, numerical experiments demonstrate the superior performance of our QML-IB algorithm compared to the state-of-the-art algorithm.

For any image watermarking algorithm, how to achieve the trade-off among robustness, imperceptibility, and watermark capacity is a challenging problem because of their mutually constrained relationship. In this paper, we design a statistical-based image watermarking system to solve the trade-off problem. In embedding process, consider the imperceptibility and the robustness, we inventively combine the undecimated dual tree complex Wavelet transform (UDTCWT) and the polar harmonic Fourier moments (PHFMs) to obtain the UDTCWT-PHFMs magnitudes as the watermark carriers, and we embed watermark signals in multiplicative manner. In modeling phase, by analyzing the statistical property and the multiple correlations of the UDTCWT-PHFMs magnitudes, we bound the magnitudes of different directions into the vector groups, and then we model them with the vector Roy type bivariate Weibull (BW-Type R) distribution so that we can capture accurately the marginal characteristics, the inter-scale dependencies, and the inter-orientation dependencies at the same time. Moreover, we obtain the model parameters with the double looped maximum likelihood estimation (double-looped MLE). Benefit from the reliable modeling result, we finally derive a novel specific image watermark decoder to blindly extract the hidden watermarks. Extensive experiment results declare the designed statistical image watermarking system achieves the better balance among imperceptibility, robustness, and payload.

Digital watermarking has been proposed as an effective technology of copyright protection and content authentication, yet up to now, research on the robust watermarking against geometric attacks is still a challenging task. This paper presents a novel robust watermarking algorithm in nonsubsampled shearlet transform (NSST) domain using quaternion polar harmonic transform (PHT) and least squares support vector regression (LS-SVR), which is a recently developed geometric correction algorithm for digital color image. The major innovative works of the proposed approach lie in that (1) the NSST is applied to embed the watermark, which can provide the image function with nearly optimal approximation and employ fully the properties of human visual system (HVS), (2) the robust 2D transform, namely quaternion PHT is introduced to represent the characteristics of color image, and (3) the novel synchronous correction method is proposed using the excellent LS-SVR and quaternion PHTs, which can accurately estimate the geometric distortions parameters. In our experiments, we applied the proposed method to the standard color image test dataset, and the experimental results demonstrate that the proposed algorithm is not only invisible, but also robustness against common signal processing operations and geometric attacks.

It is a challenging work to design a robust color image watermarking scheme against geometric distortions. Moments and moment invariants have become a powerful tool in robust image watermarking owing to their image description capability and geometric invariance property. However, the existing moment-based watermarking schemes were mainly designed for gray images but not for color images, and detection quality and robustness will be lowered when watermark is directly embedded into the luminance component or three color channels of color images. Furthermore, the imperceptibility of the embedded watermark is not well guaranteed. Based on algebra of quaternions and polar harmonic transform (PHT), we introduced the quaternion polar harmonic transform (QPHT) for invariant color image watermarking in this article, which can be seen as the generalization of PHT for gray-level images. It is shown that the QPHT can be obtained from the PHT of each color channel. We derived and analyzed the rotation, scaling, and translation (RST) invariant property of QPHT. We also discussed the problem of color image watermarking using QPHT. Experimental results are provided to illustrate the efficiency of the proposed color image watermarking against geometric distortions and common image processing operations (including color attacks).

Geometric distortions that cause displacement between embedding and detection are usually difficult for watermark to survive. It is a challenging work to design a robust image watermarking scheme against geometric distortions, especially for local geometric distortions. Based on probability density and complex angular radial transform theory, a new image watermarking algorithm robust to geometric distortions is proposed in this paper. We firstly extract the steady image feature points by using new image feature point detector, which is based on the probability density. Then we build the affine invariant local feature regions based on probability density auto-correlation matrix. And finally, we present a new image watermarking algorithm robust to geometric distortions, in which the digital watermark is embedded into the local complex angular radial transform (CART) coefficients. Experiments results show that the proposed image watermarking is not only invisible and robust against common image processing operations, but also robust against the geometric distortions.

One of the challenges in the development of a content-based image indexing and retrieval application is to achieve an efficient and robust indexing scheme. Color is a fundamental image feature used in content-based image retrieval (CBIR) systems. This paper proposes a robust and effective image retrieval scheme, which is based on the weighed color histogram of visual attention points. Firstly, the fully affine invariant visual attention points are extracted from the origin color image by using the Affine-SIFT (scale-invariant feature transform) detector. Secondly, according to the color complexity measure (CCM) theory, the visual weight values for the significant visual attention points are calculated to reflect the image local variation. Then, the weighed color histogram of visual attention points is constructed. Finally, the similarity between color images is computed by using the weighed color histogram of visual attention points. Experimental results show that the proposed image retrieval is not only more accurate and efficient in retrieving the user-interested images, but also yields higher retrieval accuracy than some state-of-the-art image retrieval schemes for various test DBs.

The development of a desynchronization invariant audio watermarking scheme without degrading acoustical quality is a challenging work. This paper proposes a robust audio watermarking scheme in Empirical Mode Decomposition (EMD) domain, in which the higher-order statistics and synchronization code are utilized. Firstly, the wavelet de-noising is performed on the original host audio, the de-noised digital audio is segmented, and then each segment is cut into two parts. Secondly, with the spatial watermarking technique, synchronization code is embedded into the statistics average value of audio samples in the first part. Thirdly, for the second part, EMD is performed, and a series of Intrinsic Mode Functions (IMFs) and a residual are given, and then the higher-order statistics of residual are obtained by using the Hausdorff distance. Finally, the digital watermark is embedded into the residual in EMD domain by using the higher-order statistics. Simulation results show that the proposed watermarking scheme is not only inaudible and robust against common signal processing operations such as MP3 compression, noise addition,resampling, and re-quantization etc, but also robust against the desynchronization attacks such as random cropping, amplitude variation, pitch shifting, and jittering etc.

Robust digital watermarking has been an active research topic in the last decade. As one of the promising approaches, feature point based image watermarking has attracted many researchers. However, the related work usually suffers from the following limitations: 1) The feature point detector is sensitive to texture region, and some noise feature points are always detected in the texture region. 2) The feature points focus too much on high contrast region, and the feature points are distributed unevenly. Based on Bayesian image segmentation, we propose a local geometrically invariant image watermarking scheme with good visual quality in this paper. Firstly, the Bayesian image segmentation is used to segment the host image into several homogeneous regions. Secondly, for each homogeneous region, image feature points are extracted using the multiscale Harris-Laplace detector, and the corresponding invariant local image regions are constructed adaptively. Finally, by taking the human visual system (HVS) into account, digital watermark is repeatedly embedded into local image regions by modulating the magnitudes of DFT coefficients. By binding the digital watermark with the invariant local image regions, the watermark detection can be done without synchronization error. Experimental results show that the proposed image watermarking is not only invisible and robust against common image processing operations such as sharpening, noise adding, and JPEG compression etc, but also robust against the geometric distortions.

On the basis of support vector regression (SVR), a new adaptive blind digital audio watermarking algorithm is proposed. This algorithm embeds the template information and watermark signal into the original audio by adaptive quantization according to the local audio correlation and human auditory masking. The procedure of watermark extraction is as follows. First, the corresponding features of template and watermark are extracted from the watermarked audio. Then, the corresponding feature of template is selected as training sample to train SVR and an SVR model is returned. Finally, the actual outputs are predicted according to the corresponding feature of watermark, and the digital watermark is recovered from the watermarked audio by using the well-trained SVR. Experimental results show that our audio watermarking scheme is not only inaudible, but also robust against various common signal processing (such as noise adding, resampling, requantization, and MP3 compression), and also has high practicability. In addition, the algorithm can extract the watermark without the help of the original digital audio signal, and the performance of it is better than other SVM audio watermarking schemes.

Synchronization is crucial to design a robust image watermarking scheme. In this paper, a novel feature-based image watermarking scheme against desynchronization attacks is proposed. The robust feature points, which can survive various signal-processing and affine transformation, are extracted by using the Harris-Laplace detector. A local characteristic region (LCR) construction method based on the scale-space representation of an image is considered for watermarking. At each LCR, the digital watermark is repeatedly embedded by modulating the magnitudes of discrete Fourier transform coefficients. In watermark detection, the digital watermark can be recovered by maximum membership criterion. Simulation results show that the proposed scheme is invisible and robust against common signal processing, such as median filtering, sharpening, noise adding, JPEG compression, etc., and desynchronization attacks, such as rotation, scaling, translation, row or column removal, cropping, and random bend attack, etc.