  Dictionary learning is a challenge topic in many image processing areas. The
basic goal is to learn a sparse representation from an overcomplete basis set.
Due to combining the advantages of generic multiscale representations with
learning based adaptivity, multiscale dictionary representation approaches have
the power in capturing structural characteristics of natural images. However,
existing multiscale learning approaches still suffer from three main
weaknesses: inadaptability to diverse scales of image data, sensitivity to
noise and outliers, difficulty to determine optimal dictionary structure. In
this paper, we present a novel multiscale dictionary learning paradigm for
sparse image representations based on an improved empirical mode decomposition.
This powerful data-driven analysis tool for multi-dimensional signal can fully
adaptively decompose the image into multiscale oscillating components according
to intrinsic modes of data self. This treatment can obtain a robust and
effective sparse representation, and meanwhile generates a raw base dictionary
at multiple geometric scales and spatial frequency bands. This dictionary is
refined by selecting optimal oscillating atoms based on frequency clustering.
In order to further enhance sparsity and generalization, a tolerance dictionary
is learned using a coherence regularized model. A fast proximal scheme is
developed to optimize this model. The multiscale dictionary is considered as
the product of oscillating dictionary and tolerance dictionary. Experimental
results demonstrate that the proposed learning approach has the superior
performance in sparse image representations as compared with several competing
methods. We also show the promising results in image denoising application.
