  We propose a novel automatic parameter selection strategy for variational
imaging problems under Poisson noise corruption. The selection of a suitable
regularization parameter, whose value is crucial in order to achieve high
quality reconstructions, is known to be a particularly hard task in low
photon-count regimes. In this work, we extend the so-called residual whiteness
principle originally designed for additive white noise to Poisson data. The
proposed strategy relies on the study of the whiteness property of a
standardized Poisson noise process. After deriving the theoretical properties
that motivate our proposal, we solve the target minimization problem with a
linearized version of the alternating direction method of multipliers, which is
particularly suitable in presence of a general linear forward operator. Our
strategy is extensively tested on image restoration and computed tomography
reconstruction problems, and compared to the well-known discrepancy principle
for Poisson noise proposed by Zanella at al. and with a nearly exact version of
it previously proposed by the authors.
