Current Development in Theory and Applications of Wavelets
Volume 1, Issue 1, Pages 31 - 56
(April 2007)
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NON-CONVEX VARIATIONAL DENOISING OF IMAGES : INTERPOLATION BETWEEN HARD AND SOFT WAVELET SHRINKAGE
Dirk A. Lorenz (Germany)
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Abstract:
Wavelet shrinkage methods are applied for denoising and estimation very successfully since more than one decade. An interesting fact about wavelet shrinkage is that there are many different motivations for shrinkage methods, namely from the areas of statistical estimation, from scale space theory, from non-linear approximation and from variational analysis.
In this paper we adopt the last viewpoint. Based on results of Chambolle et al. from the 1990s we show how soft as well as hard shrinkage can be motivated by variational denoising methods. Especially we deal with non-convex minimization problems and show that soft and hard wavelet shrinkage can be treated in the same framework. This approach will lead to a “natural” interpolation between soft and hard shrinkage.
Furthermore we illustrate the equivalence of the variational approach to denoising and the Bayes estimation approach. |
| Keywords and phrases: wavelet shrinkage, variational denoising, proximal mappings. |
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