Multilevel dictionary learning for sparse representation of images

Adaptive data-driven dictionaries for sparse approximations provide superior performance compared to predefined dictionaries in applications involving representation and classification of data. In this paper, we propose a novel algorithm for learning global dictionaries particularly suited to the sparse representation of natural images. The proposed algorithm uses a hierarchical energy based learning approach to learn a multilevel dictionary. The atoms that contribute the most energy to the representation are learned in the first level and those that contribute lesser energies are learned in the subsequent levels. The learned multilevel dictionary is compared to a dictionary learned using the K-SVD algorithm. Reconstruction results using a small number of non-zero coefficients demonstrate the advantage of exploiting energy hierarchy using multilevel dictionaries, pointing to potential applications in low bit-rate image compression. Superior performance in compressed sensing using optimized sensing matrices with small number of measurements is also demonstrated.