Correction to: Solution methods for linear discrete ill-posed problems for color image restoration

摘要

This work discusses four algorithms for the solution of linear discrete ill-posed problems with several right-hand side vectors. These algorithms can be applied, for instance, to multi-channel image restoration when the image degradation model is described by a linear system of equations with multiple right-hand sides that are contaminated by errors. Two of the algorithms are block generalizations of the standard Golub-Kahan bidiagonalization method with the block size equal to the number of channels. One algorithm uses standard Golub-Kahan bidiagonalization without restarts for all right-hand sides. These schemes are compared to standard Golub-Kahan bidiagonalization applied to each right-hand side independently. Tikhonov regularization is used to avoid severe error propagation. Numerical examples illustrate the performance of these algorithms. Applications include the restoration of color images.