Sparse Image Representation with Epitomes

Sparse coding, which is the decomposition of a vector using only a few basis elements, is widely used in machine learning and image processing. The basis set, also called dictionary, is learned to adapt to specific data. This approach has proven to be very effective in many image processing tasks. Traditionally, the dictionary is an unstructured "flat" set of atoms. In this paper, we study structured dictionaries which are obtained from an epitome, or a set of epitomes. The epitome is itself a small image, and the atoms are all the patches of a chosen size inside this image. This considerably reduces the number of parameters to learn and provides sparse image decompositions with shiftinvariance properties. We propose a new formulation and an algorithm for learning the structured dictionaries associated with epitomes, and illustrate their use in image denoising tasks.Comment: Computer Vision and Pattern Recognition, Colorado Springs : United States (2011

Learning the Morphological Diversity

International audienceThis article proposes a new method for image separation into a linear combination of morphological components. Sparsity in global 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 global and local sparsity priors together with the data fidelity 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