Analysis of the DCS one-stage Greedy Algorothm for Common Sparse Supports

where each θj is supported only on Ω ⊂ {1, 2, . . . , N}, with |Ω| = K. The matrix Ψ is orthonormal, with dimension N × N (we consider only signals sparse in an orthonormal basis). We denote by Φj the measurement matrix for signal j, where Φj is of dimension M ×N , where M < N . We let yj = Φjxj = ΦjΨθj be the observations of signal j. We assume that the measurement matrix Φj is random with i.i.d entries taken from a N (0, 1) distribution. Clearly, the matrix ΦjΨ also has i.i.d N (0, 1) entries, because Ψ is orthonormal. For convenience, we assume Ψ to be identity IN×N . The results presented can be easily extended to a more general orthonormal matrix Ψ by replacing Φj with ΦjΨ.