Recovery of clustered sparse signals from compressive measurements

We introduce a new signal model, called (K,C)-sparse, to capture K-sparse signals in N dimensions whose nonzero coefficients are contained within at most C clusters, with C < K ≪ N. In contrast to the existing work in the sparse approximation and compressive sensing literature on block sparsity, no prior knowledge of the locations and sizes of the clusters is assumed. We prove that O (K + C log(N/C)) random projections are sufficient for (K,C)-model sparse signal recovery based on subspace enumeration. We also provide a robust polynomial-time recovery algorithm for (K,C)-model sparse signals with provable estimation guarantees.