Tensor Regularized Total Least Squares Methods with Applications to Image and Video Deblurring

TL;DR

This paper introduces a tensor regularized total least squares (TR-TLS) method for solving ill-conditioned tensor systems, with applications demonstrated in image and video deblurring, extending existing matrix-based approaches to tensors.

Contribution

The paper extends the RTLS method to tensor form, developing new algorithms and properties for solving tensor systems with applications in image and video processing.

Findings

TR-TLS outperforms existing methods in deblurring tasks

Numerical examples validate the effectiveness of TR-TLS

The method handles noise in both observation and mapping tensors

Abstract

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.