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

TL;DR

This paper introduces a new automatic parameter selection method for variational image reconstruction under Poisson noise, extending the residual whiteness principle to improve low photon-count imaging tasks.

Contribution

It develops a novel whiteness-based parameter selection strategy for Poisson data, with theoretical foundations and an efficient optimization algorithm.

Findings

Effective in low photon-count regimes

Outperforms existing discrepancy principles

Validated on image restoration and CT reconstruction

Abstract

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.