A Structured Dictionary Learning Method for Multi-scale Sparse Representation

In this paper, we address the problem of learning multi-scale sparse representations of natural images using structured dictionaries. Dictionaries learned by traditional algorithms have two major limitations: lack of structure and fixed size. These methods treat atoms independently from each other, and do not exploit possible relationships between them. Fixed size of atoms restricts the flexibility of representing natural images, which usually consist of complicated structure and texture. We put forward a novel approach to learn a dictionary by performing structured sparse coding under a multi-scale binary tree model of patches. Atoms of different sizes are laid out in a grouped or hierarchical fashion, which can be fully exploited by structured sparsity regularization techniques. Experiments show that both quantitative and qualitative improvements are achieved for restoration tasks. It is worth noting that our approach can be easily integrated into existing sparse representation-based applications in image processing.