A Tree-based Dictionary Learning Framework
This work addresses dictionary learning for sparse encoding in signal processing, offering a novel hierarchical framework that is incremental in its generalization of existing transforms.
The authors tackled the problem of adaptive dictionary learning for sparse encoding by organizing data into a hierarchical binary partition tree, which generalizes a discrete Haar wavelet transform and allows incorporation of prior knowledge. The result is a structured dictionary where atoms closer to the root node tend to have greater coefficients in image patch reconstruction using Orthogonal Matching Pursuit.
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary partition tree representing a multiscale structure. The dictionary atoms are defined adaptively based on the data clusters in the partition tree. This approach can be interpreted as a generalization of a discrete Haar wavelet transform. Furthermore, any prior knowledge on the wanted structure of the dictionary elements can be simply incorporated. The computational complexity of our proposed algorithm depends on the employed clustering method and on the chosen similarity measure between data points. Thanks to the multiscale properties of the partition tree, our dictionary is structured: when using Orthogonal Matching Pursuit to reconstruct patches from a natural image, dictionary atoms corresponding to nodes being closer to the root node in the tree have a tendency to be used with greater coefficients.