Grassmannian fusion frames and its use in block sparse recovery

• We highlight the use of Grassmannian fusion frames in block sparse signal processing.
• We present a method of construction of Grassmannian fusion frames from optimal Grassmannian frames.
• A lower bound on the block coherence of dictionaries is derived.
• The Grassmannian fusion frames constructed satisfy this bound and are hence optimal dictionaries for block sparse recovery.

Tight fusion frames which form optimal packings in Grassmannian manifolds are of interest in signal processing and communication applications. In this paper, we study optimal packings and fusion frames having a specific structure for use in block sparse recovery problems. The paper starts with a sufficient condition for a set of subspaces to be an optimal packing. Further, a method of using optimal Grassmannian frames to construct tight fusion frames which form optimal packings is given. Then, we derive a lower bound on the block coherence of dictionaries used in block sparse recovery. From this result, we conclude that the Grassmannian fusion frames considered in this paper are optimal from the block coherence point of view.