Sensing Matrix Optimization for Block-Sparse Decoding

Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a welldesigned sensing matrix can reduce the coherence between the atoms of the equivalent dictionary, and as a consequence, reduce the reconstruction error. In some applications, the signals of interest 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 leads to blocksparse representations. In this work, we propose a framework for sensing matrix design that improves the ability of blocksparse approximation techniques to reconstruct and classify signals. This method is based on minimizing a weighted sum of the inter-block coherence and the sub-block coherence of the equivalent dictionary. Our experiments show that the proposed algorithm significantly improves signal recovery and classification ability of the...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Kevin Rosenblum, Lihi Zelnik-Manor, Yonina C. Eldar
• Keywords: CORR 2010, Education, Matrix, Sensing, Welldesigned Sensing Matrix