Deblurring Images: Matrices, Spectra, and Filtering (Fundamentals of Algorithms 3) (Fundamentals of Algorithms)
An iterative method for linear discrete ill-posed problems with box constraints
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Non-negatively constrained image deblurring with an inexact interior point method
Journal of Computational and Applied Mathematics
An interior-point method for large constrained discrete ill-posed problems
Journal of Computational and Applied Mathematics
Cascadic multilevel methods for fast nonsymmetric blur- and noise-removal
Applied Numerical Mathematics
Iterative image restoration using approximate inverse preconditioning
IEEE Transactions on Image Processing
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Many questions in science and engineering give rise to linear ill-posed problems, whose solution is known to satisfy box constraints, such as nonnegativity. The solution of discretized versions of these problems is highly sensitive to perturbations in the data, discretization errors, and round-off errors introduced during the computations. It is therefore often beneficial to impose known constraints during the solution process. This paper describes a two-phase algorithm for the solution of large-scale box-constrained linear discrete ill-posed problems. The first phase applies a cascadic multilevel method and imposes the constraints on each level by orthogonal projection. The second phase improves the computed approximate solution on the finest level by an active set method. The latter allows several indices of the active set to be updated simultaneously. This reduces the computational effort significantly, when compared to standard active set methods that update one index at a time. Applications to image restoration are presented.