Multiscale dictionary learning for hierarchical sparse representation
In this paper, we propose a multiscale dictionary learning framework for hierarchical sparse representation of natural images. The proposed framework leverages an adaptive quadtree decomposition to represent structured sparsity in different scales. In dictionary learning, a tree-structured regularized optimization is formulated to distinguish and represent high-frequency details based on varying local statistics and group low-frequency components for local smoothness and structural consistency. In comparison to traditional proximal gradient method, block-coordinate descent is adopted to improve the efficiency of dictionary learning with a guarantee of recovery performance. The proposed framework enables hierarchical sparse representation by naturally organizing the trained dictionary atoms in a prespecified arborescent structure with descending scales from root to leaves. Consequently, the approximation of high-frequency details can be improved with progressive refinement from coarser to finer scales. Employed into image denoising, the proposed framework is demonstrated to be competitive with the state-of-the-art methods in terms of objective and visual restoration quality.