Section: New Results

Sparse Image Representation with Epitomes

Participants : Louise Benoît, Francis Bach.

Collaboration with: Julien Mairal (Department of Statistics, University of California, Berkeley) and Jean Ponce (Willow project-team, INRIA Paris-Rocquencourt).

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 work, 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 shift invariance 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. This work has resulted in a CVPR'11 publication [11] .