Kronecker product approximation for the total variation regularization in image restoration

In this paper, we propose a new algorithm to restore blurred and noisy images based on the total variation regularization, where the discrete associated Euler-Lagrange problem is solved by exploiting the structure of the matrices and transforming the initial problem to a generalized Sylvester linear matrix equation by using a special Kronecker product approximation. Afterwards, global Krylov subspace methods are used to solve the linear matrix equation. Numerical experiments are given to illustrate the effectiveness of the proposed method.