论文标题
多核兰斯佐斯算法及其在彩色图像处理中的应用
The Multi-Symplectic Lanczos Algorithm and Its Applications to Color Image Processing
论文作者
论文摘要
在数据科学的许多最近提出的数学模型中，原始样本的低近似值越来越重要。自然的和初始的要求是，这些表示形式继承了原始结构或属性。以此目的，我们提出了一种基于lanzcos bidiagonalization的新的多隔离方法，以计算JRS-对称矩阵的部分单数三重态。这些奇异的三联体可用于重建最佳的低级别近似值，同时保留固有的多对称性。增强的Ritz和谐波Ritz向量用于执行隐式重新启动，以获得令人满意的Bidiagonal矩阵，分别用于计算$ k $最大或最小的单数三重态。我们还将新的多透明兰开斯算法应用于颜色面部识别和彩色视频压缩和重建。数值实验表明它们优于最新算法。
Low-rank approximations of original samples are playing more and more an important role in many recently proposed mathematical models from data science. A natural and initial requirement is that these representations inherit original structures or properties. With this aim, we propose a new multi-symplectic method based on the Lanzcos bidiagonalization to compute the partial singular triplets of JRS-symmetric matrices. These singular triplets can be used to reconstruct optimal low-rank approximations while preserving the intrinsic multi-symmetry. The augmented Ritz and harmonic Ritz vectors are used to perform implicit restarting to obtain a satisfactory bidiagonal matrix for calculating the $k$ largest or smallest singular triplets, respectively. We also apply the new multi-symplectic Lanczos algorithms to color face recognition and color video compressing and reconstruction. Numerical experiments indicate their superiority over the state-of-the-art algorithms.
