@article {15760, title = {Implementation of the regularized structured total least squares algorithms for blind image deblurring}, journal = {Linear Algebra and its Applications}, volume = {391}, year = {2004}, month = {2004/11/01/}, pages = {203 - 221}, abstract = {The structured total least squares (STLS) problem has been introduced to handle problems involving structured matrices corrupted by noise. Often the problem is ill-posed. Recently, regularization has been proposed in the STLS framework to solve ill-posed blind deconvolution problems encountered in image deblurring when both the image and the blurring function have uncertainty. The kernel of the regularized STLS (RSTLS) problem is a least squares problem involving Block{\textendash}Toeplitz{\textendash}Toeplitz{\textendash}Block matrices.In this paper an algorithm is described to solve this problem, based on a particular implementation of the generalized Schur Algorithm (GSA). It is shown that this new implementation improves the computational efficiency of the straightforward implementation of GSA from O(N2.5) to O(N2), where N is the number of pixels in the image. }, keywords = {Block Toeplitz matrix, Displacement rank, Generalized Schur algorithm, Image deblurring, Structured total least squares, Tikhonov regularization}, isbn = {0024-3795}, doi = {10.1016/j.laa.2004.07.006}, url = {http://www.sciencedirect.com/science/article/pii/S0024379504003362}, author = {Mastronardi,N. and Lemmerling,P. and Kalsi,A. and O{\textquoteright}Leary,D. P and Huffel,S. Van} } @article {17726, title = {On the solution of block Hessenberg systems}, journal = {Numerical Linear Algebra with Applications}, volume = {2}, year = {1995}, month = {1995/05/01/}, pages = {287 - 296}, abstract = {This paper describes a divide-and-conquer strategy for solving block Hessenberg systems. For dense matrices the method is as efficient as Gaussian elimination; however, because it works almost entirely with the original blocks, it is much more efficient for sparse matrices or matrices whose blocks can be generated on the fly. For Toeplitz matrices, the algorithm can be combined with the fast Fourier transform.}, keywords = {block Hessenberg matrix, Block Toeplitz matrix, linear system, queue}, isbn = {1099-1506}, doi = {10.1002/nla.1680020309}, url = {http://onlinelibrary.wiley.com/doi/10.1002/nla.1680020309/abstract}, author = {Stewart, G.W.} }