论文标题
张量正规化的最小二乘法，并应用于图像和视频脱张
Tensor Regularized Total Least Squares Methods with Applications to Image and Video Deblurring
论文作者
论文摘要
当噪声不仅在观察矩阵，而且在映射矩阵中时，总的最小二乘（TLS）是求解线性方程的有效方法。此外，Tikhonov正则化被广泛用于许多不适的问题。在本文中，我们将正则最小二乘（RTL）方法从golub，Hansen和O'Leary引起的矩阵形式扩展到张量形式，提出了张量正规化的总最小二乘（TR-TLS）方法，以求解不条件的张量系统。还提供并证明了有关TR-TLS问题解决方案的属性和算法，可能与RTL的属性相似。基于此方法，探索了图像和视频脱张的某些应用程序。与现有方法相比，数值示例说明了TR-TL。
Total least squares (TLS) is an effective method for solving linear equations with the situations, when noise is not just in observation matrices but also in mapping matrices. Moreover, the Tikhonov regularization is widely used in plenty of ill-posed problems. In this paper, we extend the regularized total least squares (RTLS) method from the matrix form due to Golub, Hansen and O'Leary, to the tensor form proposing the tensor regularized total least squares (TR-TLS) method for solving ill-conditioned tensor systems of equations. Properties and algorithms about the solution of the TR-TLS problem, which might be similar to those of the RTLS, are also presented and proved. Based on this method, some applications in image and video deblurring are explored. Numerical examples illustrate the TR-TLS, compared with the existing methods.
