Nonlinear Inverse Scale Space Methods for Image Restoration

Author(s):  
Martin Burger ◽  
Stanley Osher ◽  
Jinjun Xu ◽  
Guy Gilboa
2010 ◽  
Vol 19 (10) ◽  
pp. 2774-2780 ◽  
Author(s):  
Alexander Wong ◽  
Akshaya K Mishra

2012 ◽  
Vol 12 (01) ◽  
pp. 1250003 ◽  
Author(s):  
V. B. SURYA PRASATH ◽  
ARINDAMA SINGH

Anisotropic partial differential equation (PDE)-based image restoration schemes employ a local edge indicator function typically based on gradients. In this paper, an alternative pixel-wise adaptive diffusion scheme is proposed. It uses a spatial function giving better edge information to the diffusion process. It avoids the over-locality problem of gradient-based schemes and preserves discontinuities coherently. The scheme satisfies scale space axioms for a multiscale diffusion scheme; and it uses a well-posed regularized total variation (TV) scheme along with Perona-Malik type functions. Median-based weight function is used to handle the impulse noise case. Numerical results show promise of such an adaptive approach on real noisy images.


2015 ◽  
Vol 85 (297) ◽  
pp. 179-208 ◽  
Author(s):  
Michael Moeller ◽  
Xiaoqun Zhang

Author(s):  
MIN LI ◽  
BINBIN HAO ◽  
XIANGCHU FENG

In this paper, we present a new class of iterative regularization methods in the setting of Besov spaces, which can be seen as generalizations of J. Xu's method. By incorporating translation invariant wavelet transform, minimizers of the new methods can be understood as the alternative to translation invariant wavelet shrinkage with weight that is dependent on the wavelet decomposition scale and the Besov smooth order. And we generalize the iterative regularization methods to a new class of nonlinear inverse scale spaces with scale and Besov smooth order dependent weight. The numerical results show an excellent denoising effect and improvement over J. Xu's method.


2012 ◽  
Vol 82 (281) ◽  
pp. 269-299 ◽  
Author(s):  
Martin Burger ◽  
Michael Möller ◽  
Martin Benning ◽  
Stanley Osher

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