Iterative regularization and inverse scale space methods with wave atoms

Abstract

Sparsity is playing an important role in image processing and its application fields, such as deconvolution, signal modelling and denoising, source separation and classification, as well as compressed sensing theory, etc. As one of novel computational harmonic analysis tools, wave atoms have a significantly sparser expansion of warped oscillatory functions or oriented textures than that of other fixed standard representations such as Gabor filters, wavelets and curvelets. In this article, we first propose a completely discrete iterative regularization method based on wave atoms coefficients. Also, the good monotonic properties and optimal stopping criterion are obtained, which make the denoising image sequence monotonically converge to the original one in the sense of Bregman distance. Then, a wave atoms-based inverse scale space method is presented. Finally, experimental results and comparisons show that the proposed methods can well preserve textures while removing the noise.

Keywords:

• wave atoms
• sparsity
• iterative regularization
• inverse scale space
• Bregman distance
• shrinkage

AMS Subject Classifications::

• 94A08
• 42C40
• 65K10

Acknowledgements

We would like to thank the unknown reviewers for their valuable comments and suggestions which resulted in a great improvement of the article. Authors are supported by grants from the NSFC(60872138).