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Modular solvers for image restoration problems using the discrepancy principle. (English) Zbl 1071.68557

The article presents a modular approach to the solution of constrained problems in image restoration. At each Newton-based iteration step, an unconstrained black-box solver is used. The method is presented on practical examples of denoising of grey-scale images, denoising of vector-valued (colour) images and denoising and deblurring of grey-scale images. The non-linearity inside of the total-variation functionals is treated by the primal-dual solver. Finally, the constrained and unconstrained methods are compared by means of the residual values. The article is related to the previous work by J.B.Rosen [J.Qufu Norm.Univ., Nat.Sci.18, 50-52 (1992; Zbl 0800.90742)], and by T.F.Chan, G.H.Golub and P.Mulet [12th international conference on analysis and optimization of systems, images, wavelets and PDE’s, Paris, France, June 26-28, 1996, 241-252 (1996; Zbl 0852.68114)].

MSC:

68U10 Computing methodologies for image processing
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65H10 Numerical computation of solutions to systems of equations

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