A global Lanczos method for image restoration

Image restoration often requires the solution of large linear systems of equations with a very ill-conditioned, possibly singular, matrix and an error-contaminated right-hand side. The latter represents the available blur and noise-contaminated image, while the matrix models the blurring. Computation of a meaningful restoration of the available image requires the use of a regularization method. We consider the situation when the blurring matrix has a Kronecker product structure and an estimate of the norm of the desired image is available, and illustrate that efficient restoration of the available image can be achieved by Tikhonov regularization based on the global Lanczos method, and by using the connection of the latter to Gauss-type quadrature rules.