An introduction to the mathematical theory of inverse problems
An introduction to the mathematical theory of inverse problems
Nonstationary iterated Tikhonov regularization
Journal of Optimization Theory and Applications
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
Iterative Total Variation Regularization with Non-Quadratic Fidelity
Journal of Mathematical Imaging and Vision
Inverse Scale Spaces for Nonlinear Regularization
Journal of Mathematical Imaging and Vision
Convergence of Fixed Point Iteration for Modified Restoration Problems
Journal of Mathematical Imaging and Vision
Image Super-Resolution by TV-Regularization and Bregman Iteration
Journal of Scientific Computing
An iterative method with general convex fidelity term for image restoration
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I
Primal and Dual Bregman Methods with Application to Optical Nanoscopy
International Journal of Computer Vision
Nonlinear inverse scale space methods for image restoration
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Structure-Texture decomposition by a TV-Gabor model
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Dual Norm Based Iterative Methods for Image Restoration
Journal of Mathematical Imaging and Vision
Nonlinear Multilayered Representation of Graph-Signals
Journal of Mathematical Imaging and Vision
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In this paper we derive scale space methods for inverse problems which satisfy the fundamental axioms of fidelity and causality and we provide numerical illustrations of the use of such methods in deblurring. These scale space methods are asymptotic formulations of the Tikhonov-Morozov regularization method. The analysis and illustrations relate diffusion filtering methods in image processing to Tikhonov regularization methods in inverse theory.