POISSON LOW-RANK MATRIX RECOVERY USING THE ANSCOMBE TRANSFORM

Ajit Rajwade

Abstract:

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 fluxpreservation. Besides being computationally tractable (convex), our estimator also allows for principled parameter tuning. Moreover, our method is capable of handling PoissonGaussian noise and the case where the Poisson or PoissonGaussian 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.