Whiteness-based parameter selection for Poisson data in variational image processing

Abstract

We propose a novel parameter selection strategy for variational imaging problems under Poisson noise corruption. The selection of a suitable value of the regularization parameter, which is crucial for achieving high quality reconstructions, is known to be a particularly hard task in low photon-counting 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 exploiting the whiteness property of a suitably standardized Poisson noise process. After deriving the theoretical properties underlying our proposal, we solve the target optimization problem by the alternating direction method of multipliers, in its standard two-blocks version or in a semi-linearized version depending on the imaging problem. Our strategy is extensively tested on image restoration and computed tomography reconstruction problems, and compared to the state-of-the-art discrepancy principle for Poisson noise proposed by Zanella at al. as well as to a nearly exact version of it recently proposed by the authors.