论文标题
张量Krylov子空间方法通过t-rodopoduct进行颜色图像处理
Tensor Krylov subspace methods via the T-product for color image processing
论文作者
论文摘要
本文涉及开发张量的Krylov子空间方法来求解大型多线性张量方程。我们使用众所周知的T产品来定义张量的全局Arnoldi和Tensor Global Gloub-Kahan BiDiagonalization算法。此外，我们说明了如何利用所谓的Tikhonov正则化技术来恢复模糊多通道（彩色）图像和视频而引起的基于张量的全局方法来解决不适合的问题，以提供可计算的近似正则化解决方案。我们还审查了在Tikhonov正则化中选择正则化参数的广义交叉验证和差异原理类型。给出了RGB图像和视频处理的应用，以证明算法的效率。
The present paper is concerned with developing tensor iterative Krylov subspace methods to solve large multi-linear tensor equations. We use the well-known T-product for two tensors to define tensor global Arnoldi and tensor global Gloub-Kahan bidiagonalization algorithms. Furthermore, we illustrate how tensor-based global approaches can be exploited to solve ill-posed problems arising from recovering blurry multichannel (color) images and videos, using the so-called Tikhonov regularization technique, to provide computable approximate regularized solutions. We also review a generalized cross-validation and discrepancy principle type of criterion for the selection of the regularization parameter in the Tikhonov regularization. Applications to RGB image and video processing are given to demonstrate the efficiency of the algorithms.
