Learning the Morphological Diversity

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 non-convex energy and the separation is obtained as a stationary point of this energy. This variational optimization is extended to solve more general inverse problems such as inpainting. A new adaptive morphological component analysis algorithm is derived to find a stationary point of the energy. Using adapted dictionaries learned from data allows to circumvent some difficulties faced by fixed dictionaries. Numerical results demonstrate that this adaptivity is indeed crucial to capture complex texture patterns. Key words. Adaptive morphological component analysis, sparsity, image separation, inpainting, dictionary...

• Type: Journal
• Year: 2010
• Where: SIAMIS
• Authors: Gabriel Peyré, Jalal Fadili, Jean-Luc Starck
• Keywords: Images, Morphological Component Analysis, Morphological Components, SIAMIS 2010