Nonuniform Sparse Recovery with Fusion Frames∗

Fusion frames are generalizations of classical frames that provide a richer description of signal spaces where subspaces are used in the place of vectors as signal building blocks. The main idea of this work is to extend ideas from Compressed Sensing (CS) to a fusion frame setup. We use a 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 CS. In particular we invoke a mixed `1/`2 norm minimization in order to reconstruct sparse signals. The novelty of our research is to exploit an incoherence property of the fusion frame which allows us to reduce the number of measurements needed for sparse recovery.