Algorithms for Structured Total Least Squares Problems with Applications to Blind Image Deblurring

Mastronardi, Lemmerling, and van Huel presented an algorithm for solving a total least squares problem when the matrix and its perturbations are Toeplitz. A Toeplitz matrix is a special kind of matrix with small displacement rank. Here we generalize the fast algorithm to any matrix with small displacement rank. In particular, we show how to efficiently construct the generators whenever M has small displacement rank and show that in many important cases the Cholesky factorization of the matrix M M can also be determined fast. We further extend this problem to Tikhonov regularization of ill-posed problems and illustrate the use of the algorithm on an image deblurring problem.