Sparsity-based single-channel blind separation of superimposed AR processes

We address the blind separation of two autoregressive (AR) processes from a single mixture thereof, when their respective driving-noise (“innovation”) sequences are known to be temporally sparse. Unlike other single-channel separation schemes, which use dictionary-learning, our method essentially estimates the sparsifying transformation of each source directly from the observed mixture (by estimating the respective AR parameters), and therefore does not require a training stage. We cast the problem as a constrained, non-convex ℓ₁-norm minimization and propose an iterative solution scheme, which iterates between linear-programming-based estimation of the respective driving-sequences given estimates of the AR parameters, and gradient-based refinement of the estimated AR parameters given the estimated driving sequences. Near-perfect separation is demonstrated using a simulated example.