Reconstructing Signals from a Union of Linear Subspaces Using a Generalized CoSaMP

where A is an m×n matrix with entries independently drawn from the standard normal distribution and e ∈ R represents the noise. We assume that the noise does not depend on A, and that its energy is bounded. Further, we assume that m < n. As in this case recovering x from y becomes an ill-posed problem, an additional prior on x is required. We rely on a general signal model a union of low dimensional linear subspaces [1]–[3]. More specifically, we assume that a possibly infinite set of finite-dimensional subspaces S = {Vi} is given, and that the signal belongs to one of the subspaces in S, i.e., x ∈ V0, and V0 ∈ S. However, this subspace is unknown. We define the B-order sum for the set S, with an integer B ≥ 1, as