Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Inverse Scale Space Theory for Inverse Problems
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Image Processing via the Beltrami Operator
ACCV '98 Proceedings of the Third Asian Conference on Computer Vision-Volume I - Volume I
Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (Mps-Siam Series on Optimization 6)
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
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
Noise removal using smoothed normals and surface fitting
IEEE Transactions on Image Processing
Original Article: A new nonlocal total variation regularization algorithm for image denoising
Mathematics and Computers in Simulation
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Error minimization of global functionals provides a natural setting for analyzing image processing and regularization. This approach leads to scale spaces, which in the continuous formulation are the solution of nonlinear partial differential equations. In this work we derive properties for a class of inverse scale space methods. The main contribution of this paper is the development of a proof that the methods considered are convergent for convex regularization operators. The proof is based on energy methods and the Bregman distance. Further, estimates for convergence toward a clean image with noisy forcing data is provided in terms of both the L 2 norm and Bregman distances. This leads to natural estimates of optimal stopping scale for the inverse scale space method. These analytical results are discussed in the context of a numerical example.