Zhi-Gang Jia

Mei-Xiang Zhao, Zhi-Gang Jia, Dun-Wei Gong et al.

A new data-driven bilateral generalized two-dimensional quaternion principal component analysis (BiG2DQPCA) is presented to extract the features of matrix samples from both row and column directions. This general framework directly works on the 2D color images without vectorizing and well preserves the spatial and color information, which makes it flexible to fit various real-world applications. A generalized ridge regression model of BiG2DQPCA is firstly proposed with orthogonality constrains on aimed features. Applying the deflation technique and the framework of minorization-maximization, a new quaternion optimization algorithm is proposed to compute the optimal features of BiG2DQPCA and a closed-form solution is obtained at each iteration. A new approach based on BiG2DQPCA is presented for color face recognition and image reconstruction with a new data-driven weighting technique. Sufficient numerical experiments are implemented on practical color face databases and indicate the superiority of BiG2DQPCA over the state-of-the-art methods in terms of recognition accuracies and rates of image reconstruction.

Yong Chen, Zhi-Gang Jia, Ya-Xin Peng et al.

Quaternion singular value decomposition (QSVD) is a robust technique of digital watermarking which can extract high quality watermarks from watermarked images with low distortion. In this paper, QSVD technique is further investigated and an efficient robust watermarking scheme is proposed. The improved algebraic structure-preserving method is proposed to handle the problem of "explosion of complexity" occurred in the conventional QSVD design. Secret information is transmitted blindly by incorporating in QSVD two new strategies, namely, coefficient pair selection and adaptive embedding. Unlike conventional QSVD which embeds watermarks in a single imaginary unit, we propose to adaptively embed the watermark into the optimal hiding position using the Normalized Cross-Correlation (NC) method. This avoids the selection of coefficient pair with less correlation, and thus, it reduces embedding impact by decreasing the maximum modification of coefficient values. In this way, compared with conventional QSVD, the proposed watermarking strategy avoids more modifications to a single color image layer and a better visual quality of the watermarked image is observed. Meanwhile, adaptive QSVD resists some common geometric attacks, and it improves the robustness of conventional QSVD. With these improvements, our method outperforms conventional QSVD. Its superiority over other state-of-the-art methods is also demonstrated experimentally.

Zhi-Gang Jia, Zi-Jin Qiu, Qian-Yu Wang et al.

One of the most powerful methods of color image recognition is the two-dimensional principle component analysis (2DQPCA) approach, which is based on quaternion representation and preserves color information very well. However, the current versions of 2DQPCA are still not feasible to extract different geometric properties of color images according to practical data analysis requirements and they are vulnerable to strong noise. In this paper, a generalized 2DQPCA approach with weighting is presented with imposing $L_{p}$ norms on both constraint and objective functions. As a unit 2DQPCA framework, this new version makes it possible to choose adaptive regularizations and constraints according to actual applications and can extract both geometric properties and color information of color images. The projection vectors generated by the deflating scheme are required to be orthogonal to each other. A weighting matrix is defined to magnify the effect of main features. This overcomes the shortcomings of traditional 2DQPCA that the recognition rate decreases as the number of principal components increases. The numerical results based on the real face databases validate that the newly proposed method is robust to noise and performs better than the state-of-the-art 2DQPCA-based algorithms and four prominent deep learning methods.

Xiao Chen, Zhi-Gang Jia, Yunfeng Cai et al.

A relaxed two dimensional principal component analysis (R2DPCA) approach is proposed for face recognition. Different to the 2DPCA, 2DPCA-$L_1$ and G2DPCA, the R2DPCA utilizes the label information (if known) of training samples to calculate a relaxation vector and presents a weight to each subset of training data. A new relaxed scatter matrix is defined and the computed projection axes are able to increase the accuracy of face recognition. The optimal $L_p$-norms are selected in a reasonable range. Numerical experiments on practical face databased indicate that the R2DPCA has high generalization ability and can achieve a higher recognition rate than state-of-the-art methods.