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
Keyword(s):  
Scale Space ◽  
Iterative Regularization ◽  
Inverse Scale Space

ITERATIVE REGULARIZATION AND NONLINEAR INVERSE SCALE SPACE BASED ON TRANSLATION INVARIANT WAVELET SHRINKAGE

2008 ◽  
Vol 06 (01) ◽  
pp. 83-95 ◽  
Author(s):  
MIN LI ◽  
BINBIN HAO ◽  
XIANGCHU FENG
Keyword(s):  
Wavelet Decomposition ◽  
Scale Space ◽  
Regularization Methods ◽  
Wavelet Shrinkage ◽  
Iterative Regularization ◽  
Translation Invariant ◽  
New Class ◽  
New Methods ◽  
Scale Spaces ◽  
Inverse Scale Space

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.

Iterative regularization and inverse scale space methods with wave atoms

2010 ◽  
Vol 90 (8) ◽  
pp. 1215-1225
Author(s):  
Xiangchu Feng ◽  
Guojun Liu ◽  
Weiwei Wang
Keyword(s):  
Scale Space ◽  
Iterative Regularization ◽  
Wave Atoms ◽  
Inverse Scale Space

Fast sparse reconstruction: Greedy inverse scale space flows

2015 ◽  
Vol 85 (297) ◽  
pp. 179-208 ◽  
Author(s):  
Michael Moeller ◽  
Xiaoqun Zhang
Keyword(s):  
Scale Space ◽  
Sparse Reconstruction ◽  
Inverse Scale Space

scholarly journals An adaptive inverse scale space method for compressed sensing

2012 ◽  
Vol 82 (281) ◽  
pp. 269-299 ◽  
Author(s):  
Martin Burger ◽  
Michael Möller ◽  
Martin Benning ◽  
Stanley Osher
Keyword(s):  
Compressed Sensing ◽  
Scale Space ◽  
Space Method ◽  
Inverse Scale Space
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