Sparse Recovery of Fusion Frame Structured Signals

Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from a fusion frame. We use a block sparsity model for fusion frames and then show that sparse signals under this model can be compressively sampled and reconstructed in ways similar to standard Compressed Sensing (CS). In particular we invoke a mixed `1/`2 norm minimization in order to reconstruct sparse signals. In our work, we show that assuming a certain incoherence property of the subspaces and the apriori knowledge of it allows us to improve recovery when compared to the usual block sparsity case.