Learning Structured Dictionaries for Image Representation

The dictionary approach to signal and image processing has been massively investigated in the last two decades, proving very attractive for a wide range of applications. The effectiveness of dictionary-based methods, however, is strongly influenced by the choice of the set of basis functions. Moreover the structure of the dictionary is of paramount importance regarding efficient implementation and practical applications such as image coding. In this work, an overcomplete code for sparse representation of natural images has been learnt from a set a real-world scenes. Experiments have been carried out using images of different sizes in order to check the influence of this parameter on the learnt bases. The functions found have been organized into a hierarchical structure. We take advantage of this representation of the dictionary, adopting a tree-structured greedy algorithm to build sparse approximations of images. Using this procedure, no a-priori constraint is imposed on the structure of the dictionary, allowing great flexibility in its design and lower computational complexity.