Iterative Regularization and Nonlinear Inverse Scale Space Applied to Wavelet-Based Denoising

2007 ◽  
Vol 16 (2) ◽  
pp. 534-544 ◽  
Author(s):  
Jinjun Xu ◽  
Stanley Osher
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.


2010 ◽  
Vol 90 (8) ◽  
pp. 1215-1225
Author(s):  
Xiangchu Feng ◽  
Guojun Liu ◽  
Weiwei Wang

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

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

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