To address the non-negativity dropout problem of quaternion models, a novel quasi non-negative quaternion matrix factorization (QNQMF) model is presented for color image processing. To implement QNQMF, the quaternion projected gradient algorithm and the quaternion alternating direction method of multipliers are proposed via formulating QNQMF as the non-convex constraint quaternion optimization problems. Some properties of the proposed algorithms are studied. The numerical experiments on the color image reconstruction show that these algorithms encoded on the quaternion perform better than these algorithms encoded on the red, green and blue channels. Furthermore, we apply the proposed algorithms to the color face recognition. Numerical results indicate that the accuracy rate of face recognition on the quaternion model is better than on the red, green and blue channels of color image as well as single channel of gray level images for the same data, when large facial expressions and shooting angle variations are presented.

翻译：为了解决四环模型的非负退出问题,为色彩图像处理提供了一个新型的准非负四环矩阵因子化模型。为了实施 QNMF,建议采用四环预测梯度算法和四环交替方向乘数法,办法是将QNQMF作为非convex制约四环优化问题。研究了拟议算法的某些特性。关于彩色图像重建的数字实验显示,在四环上编码的这些算法比在红、绿和蓝通道上编码的算法效果更好。此外,我们将提议的算法应用于颜色面部识别。数字结果显示,四环模型的面孔识别准确率比红、绿和蓝色彩色图像以及同一数据的灰色图像单一通道的准确度要好,当显示大面部表达和射击角度变化时。