Low-rank matrix recovery with poison noise

In this paper, we present a regularized maximum likelihood estimator to recover an approximately low-rank matrix under Poisson noise. We also establish performance bounds for the proposed estimator, by combining techniques for recovering sparse signals under Poisson noise [2], and methods for recovering low-rank matrices [3]. Our bound demonstrates that as the overall intensity of the signal increases, the upper bound on the risk performance of proposed estimator decays at certain rate depending how well the image can be approximated by a low-rank matrix. On the other hand, our bound also indicates there is certain threshold effect such that the risk might not monotonically decrease with respect to the number of measurements, in line with the result in compressed sensing.