Separation of a subspace-sparse signal: Algorithms and conditions

In this paper, we show how two classical sparse recovery algorithms, orthogonal matching pursuit and basis pursuit, can be naturally extended to recover block-sparse solutions for subspace-sparse signals. A subspace-sparse signal is sparse with respect to a set of subspaces, instead of atoms. By generalizing the notion of mutual incoherence to the set of subspaces, we show that all classical sufficient conditions remain exactly the same for these algorithms to work for subspace-sparse signals, in both noiseless and noisy cases. The sufficient conditions provided are easy to verify for large systems. We conduct simulations to compare the performance of the proposed algorithms.