  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 well-designed 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 block-sparse representations. In this work, we propose a framework for
sensing matrix design that improves the ability of block-sparse 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 Block-OMP algorithm compared to sensing matrix optimization methods that do
not employ block structure.
