Dictionary Optimization for Block-Sparse Representations

Recent work has demonstrated that using a carefully designed dictionary instead of a predefined one, can improve the sparsity in jointly representing a class of signals. This has motivated the derivation of learning methods for designing a dictionary which leads to the sparsest representation for a given set of signals. In some applications, the signals of interest can have further structure, so that they can be well approximated by a union of a small number of subspaces (e.g., face recognition and motion segmentation). This implies the existence of a dictionary which enables block-sparse representations of the input signals once its atoms are properly sorted into blocks. In this paper, we propose an algorithm for learning a block-sparsifying dictionary of a given set of signals. We do not require prior knowledge on the association of signals into groups (subspaces). Instead, we develop a method that automatically detects the underlying block structure. This is achieved by iteratively ...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Kevin Rosenblum, Lihi Zelnik-Manor, Yonina C. Eldar
• Keywords: Block Structure, CORR 2010, Education, Motion Segmentation, Sparsest Representation