Memory-Limited stochastic approximation for poisson subspace tracking

Poisson noise is ubiquitously encountered in applications including medical and photon-limited imaging. We consider the problem of recovering and tracking the underlying Poisson rate, where the rate vector is assumed to lie in an unknown low-dimensional subspace, with possibly missing entries. A stochastic approximation (SA) algorithm is proposed to solve the problem. This algorithm alternates between two steps. It sequentially identifies the underlying subspace, and recovers coefficients associated with the subspace. The SA algorithm is then modified to obtain a memory-efficient algorithm without storing all historic data. Two theoretical performance guarantees are establish regarding the convergence of SA algorithm. Numerical experiments are provided to demonstrate the proposed algorithms for Poisson video. The memory-limited SA algorithm is shown to empirically yield similar performances to the original SA algorithm.