Learning the Morphological Diversity

@article{Peyr2010LearningTM,
  title={Learning the Morphological Diversity},
  author={Gabriel Peyr{\'e} and Mohamed-Jalal Fadili and Jean-Luc Starck},
  journal={SIAM J. Imaging Sci.},
  year={2010},
  volume={3},
  pages={646-669}
}
This article proposes a new method for image separation into a linear combination of morphological components. Sparsity in fixed dictionaries is used to extract the cartoon and oscillating content of the image. Complicated texture patterns are extracted by learning adapted local dictionaries that sparsify patches in the image. These fixed and learned sparsity priors define a nonconvex energy, and the separation is obtained as a stationary point of this energy. This variational optimization is… 
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