Krylov子空间方法及在基于图像的生物特征识别中的应用

随着科技的发展，基于图像的生物特征识别技术已经被广泛的应用于身份识别和信息安全领域。但在互联网时代，该技术所需要处理的数据量越来越大，而由于计算机的存储量和运算速度的限制，传统的算法已经不能满足识别技术当中的实时性要求。为了解决这个问题，在本项目中，我们将Krylov子空间方法与基于图像的生物特征识别技术相结合。本项目拟做以下主要研究：（1）对传统的Krylov子空间方法进行创新和改进，并证明改进算法的收敛性，讨论其误差界，投影向量的正交性以及重启等问题；（2）将改进的算法应用于基于图像的生物特征识别技术的数据存储、特征提取及分类识别中；（3）将Krylov子空间方法在矩阵方面的一些研究成果推广到高阶张量中，并将其应用于三维图像生物识别中。本项目中所涉及的所有方法都将设计成具体的算法，并且都会用数值实验来检验其有效性及理论分析的正确性。

With the development of science and technology, image biometric technology has been widely used in the field of information security and identity recognition. In the internet age, the datasets become larger and larger, due to the limitation of computer storage and computing speed, old methods cannot meet the need of real-time requirements in biometrics. To solve this problem, we apply Krylov subspace methods to image biometric technology. So, in this project we will study: (1) improving the classical Krylov subspace methods innovatively, proving the convergence, discussing error bounds, the orthogonality of the projection vectors and the restarted problems of the new methods; (2) applying the new methods to the data storage, feature extraction and classification; (3) deducing some research results from matrix to higher-order tensor, and applying the new methods to 3-order tensor image biometric. All new methods involved in this project will be desigend to algorithms, the efficiency and the correct of theoretic analysis will be proved from numerical experiments.