Tensorial conditional gradient method for solving multidimensional ill-posed problems

We consider solving a class of tensorial ill-conditioned problems. This problem is treated as a convex constrained minimization problem. This kind of ill-conditioned problems appears in several applications as color images and video restoration. A new tensor degradation model to recover color image and video from blur and noise is given. Tikhonov regularization approach is used to reduce the effect of noise in the computed solution. This approach leads to a convex tensor minimization problem, that can be solved basing on the conditional gradient method. We adapted the Generalized Cross Validation method to the tensorial model for appropriate choice of the regularization parameter. Numerical tests for image and video restoration are given to illustrate the effectiveness of the proposed approach compared with the classical method. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This study focuses on solving a class of tensorial ill-conditioned problems by formulating them as convex constrained minimization problems. The proposed approach introduces a new tensor degradation model and utilizes Tikhonov regularization to reduce the impact of noise in color image and video restoration. The tensor minimization problem is solved using the conditional gradient method. The Generalized Cross Validation method is adapted for appropriate selection of the regularization parameter in the tensorial model. Experimental results demonstrate the effectiveness of the proposed approach compared to classical methods.