Construction of an adaptive multiresolution dictionary for sparse representations.

Driven by advances in the field of acquisition technology and image processing during the last decade applications tend to use more high resolution data. The features, patterns or structures of interest are "hidden" in these enormous volumes of data. When the data contains many instances of objects of similar nature, they can often be represented succinctly by using a customized dictionary, which has to be learned from the data. The customization happens by selecting existing building blocks that reflect the geometrical nature of the content, and combining them appropriately into specially adapted atoms. We propose a multiresolution approach to the learning of these atoms, with coarse, large atoms being learned first, followed by gradually finer scale atoms. We expect this to be more efficient than fixed-size-atom dictionaries. In addition, the tree structure obtained in the process of building the multiresolution dictionary already characterizes the data to some extent, and we will study how this structure relates to or changes with the data. As a case study for this approach we will analyze high resolution and multimodal representations of paintings of our cultural heritage.