POISSON LOW-RANK MATRIX RECOVERY USING THE ANSCOMBE TRANSFORM

摘要

We present an estimator, based on the Anscombe transform, for the problem of low-rank matrix recovery under Poisson noise. We derive an upper bound on the matrix reconstruction error for this estimator, considering a linear sensing operator which obeys realistic constraints like non-negativity and flux-preservation. Besides being computationally tractable (convex), our estimator also allows for principled parameter tuning. Moreover, our method is capable of handling Poisson-Gaussian noise and the case where the Poisson or Poisson-Gaussian corrupted measurements are uniformly quantized. In addition to our theoretical results, we present some numerical results for Poisson low-rank matrix recovery under varying intensity levels and number of measurements.