A Novel Wasserstein Quaternion Generative Adversarial Network for Color Image Generation

Color image generation has a wide range of applications, but the existing generation models ignore the correlation among color channels, which may lead to chromatic aberration problems. In addition, the data distribution problem of color images has not been systematically elaborated and explained, so that there is still the lack of the theory about measuring different color images datasets. In this paper, we define a new quaternion Wasserstein distance and develop its dual theory. To deal with the quaternion linear programming problem, we derive the strong duality form with helps of quaternion convex set separation theorem and quaternion Farkas lemma. With using quaternion Wasserstein distance, we propose a novel Wasserstein quaternion generative adversarial network. Experiments demonstrate that this novel model surpasses both the (quaternion) generative adversarial networks and the Wasserstein generative adversarial network in terms of generation efficiency and image quality.

Quaternion Generative Adversarial Neural Networks and Applications to Color Image Inpainting

Color image inpainting is a challenging task in imaging science. The existing method is based on real operation, and the red, green and blue channels of the color image are processed separately, ignoring the correlation between each channel. In order to make full use of the correlation between each channel, this paper proposes a Quaternion Generative Adversarial Neural Network (QGAN) model and related theory, and applies it to solve the problem of color image inpainting with large area missing. Firstly, the definition of quaternion deconvolution is given and the quaternion batch normalization is proposed. Secondly, the above two innovative modules are applied to generate adversarial networks to improve stability. Finally, QGAN is applied to color image inpainting and compared with other state-of-the-art algorithms. The experimental results show that QGAN has superiority in color image inpainting with large area missing.

A New Cross-Space Total Variation Regularization Model for Color Image Restoration with Quaternion Blur Operator

The cross-channel deblurring problem in color image processing is difficult to solve due to the complex coupling and structural blurring of color pixels. Until now, there are few efficient algorithms that can reduce color infection in deblurring process. To solve this challenging problem, we present a novel cross-space total variation (CSTV) regularization model for color image deblurring by introducing a quaternion blur operator and a cross-color space regularization functional. The existence and uniqueness of the solution is proved and a new L-curve method is proposed to find a sweet balance of regularization functionals on different color spaces. The Euler-Lagrange equation is derived to show that CSTV has taken into account the coupling of all color channels and the local smoothing within each color channel. A quaternion operator splitting method is firstly proposed to enhance the ability of color infection reduction of the CSTV regularization model. This strategy also applies to the well-known color deblurring models. Numerical experiments on color image databases illustrate the efficiency and manoeuvrability of the new model and algorithms. The color images restored by them successfully maintain the color and spatial information and are of higher quality in terms of PSNR, SSIM, MSE and CIEde2000 than the restorations of the-state-of-the-art methods.

Advanced Variations of Two-Dimensional Principal Component Analysis for Face Recognition

The two-dimensional principal component analysis (2DPCA) has become one of the most powerful tools of artificial intelligent algorithms. In this paper, we review 2DPCA and its variations, and propose a general ridge regression model to extract features from both row and column directions. To enhance the generalization ability of extracted features, a novel relaxed 2DPCA (R2DPCA) is proposed with a new ridge regression model. R2DPCA generates a weighting vector with utilizing the label information, and maximizes a relaxed criterion with applying an optimal algorithm to get the essential features. The R2DPCA-based approaches for face recognition and image reconstruction are also proposed and the selected principle components are weighted to enhance the role of main components. Numerical experiments on well-known standard databases indicate that R2DPCA has high generalization ability and can achieve a higher recognition rate than the state-of-the-art methods, including in the deep learning methods such as CNNs, DBNs, and DNNs.

Sample-Relaxed Two-Dimensional Color Principal Component Analysis for Face Recognition and Image Reconstruction

A sample-relaxed two-dimensional color principal component analysis (SR-2DCPCA) approach is presented for face recognition and image reconstruction based on quaternion models. A relaxation vector is automatically generated according to the variances of training color face images with the same label. A sample-relaxed, low-dimensional covariance matrix is constructed based on all the training samples relaxed by a relaxation vector, and its eigenvectors corresponding to the $r$ largest eigenvalues are defined as the optimal projection. The SR-2DCPCA aims to enlarge the global variance rather than to maximize the variance of the projected training samples. The numerical results based on real face data sets validate that SR-2DCPCA has a higher recognition rate than state-of-the-art methods and is efficient in image reconstruction.