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The problem of QR decomposition is considered one of the fundamental problems commonly encountered in both scientific research and engineering applications. In this paper, the QR decomposition for complex-valued time-varying matrices is analyzed and investigated. Specifically, by applying the zeroing neural dynamics (ZND) method, dimensional reduction method, equivalent transformations, Kronecker product, and vectorization techniques, a new continuous-time QR decomposition (CTQRD) model is derived and presented. Then, a novel eleven-instant Zhang et al discretization (ZeaD) formula, with fifth-order precision, is proposed and studied. Additionally, five discrete-time QR decomposition (DTQRD) models are further obtained by using the eleven-instant and other ZeaD formulas. Theoretical analysis and numerical experimental results confirmed the correctness and effectiveness of the proposed continuous and discrete ZND models.

This paper addresses the median filtering forensics for a lossy compressed image with low resolution, which is essential for the identification of fake images and fake videos. A deep residual model with training data augmentation is employed in the proposed method. To solve the dilemma that the low-resolution image is the lack of enough statistical pixels for extracting reliable features, we propose a filter layer to widen the inputs for the convolutional neural network (CNN). First, we perform the high-pass filtering to an image in the filtered layer and stack the multiple filtered residuals into 16-channel feature maps as inputs of CNN. Then, a deep residual CNN model has proposed to self-learn the median filtering traces that are hidden in the JPEG lossy compressed image. To alleviate the over-fitting issue of the deeper CNN model, we employ a data augmentation scheme in the training to increase the diversity of training data and, thus, obtain a more stable median filtering detector. The experimental results demonstrate that the proposed net with training data augmentation outperforms state of the arts in both baseline test and generalization ability test, achieving at least 2% higher in terms of detection accuracy.

Existing video steganography puts much emphasis on the design of algorithms such as mapping rules or distortion functions, thereby ignoring the selection of cover to embed secret information. However, this is just one of the major differences between image steganography and video steganography. In addition, since HEVC is the latest standard in the video codec field, it is of important academic significance and applied value to study HEVC-based steganography. This paper proposes a novel video steganography in HEVC, based on intra-prediction mode (IPM). Firstly, this paper analyzes the probability distribution of 4 × 4 IPMs. Then a cover selection rule combined with the Coding Unit (CU) and Prediction Unit (PU) coding information is proposed, which can improve the security performance of a stego video stream. In addition, matrix coding is used as a coding example to implement the steganography on HEVC video streams. Experimental results show that the proposed algorithm can not only maintain the video quality and the security performance but is also easy to implement. Furthermore, the proposed cover selection rule can also be integrated into other HEVC IPM based steganography.

Image resampling is a common manipulation in image processing. The forensics of resampling plays an important role in image tampering detection, steganography, and steganalysis. In this paper, we proposed an effective and secure detector, which can simultaneously detect resampling and its forged resampling which is attacked by antiforensic schemes. We find that the interpolation operation used in the resampling and forged resampling makes these two kinds of image show different statistical behaviors from the unaltered images, especially in the high frequency domain. To reveal the traces left by the interpolation, we first apply multidirectional high-pass filters on an image and the residual to create multidirectional differences. Then, the difference is fit into an autoregressive (AR) model. Finally, the AR coefficients and normalized histograms of the difference are extracted as the feature. We assemble the feature extracted from each difference image to construct the comprehensive feature and feed it into support vector machines (SVM) to detect resampling and forged resampling. Experiments on a large image database show that the proposed detector is effective and secure. Compared with the state-of-the-art works, the proposed detector achieved significant improvements in the detection of downsampling or resampling under JPEG compression.