To e or not to e in poisson image reconstruction

In photon-limited image reconstruction, observations can be modeled as y ~ Poisson(f), where f := e^g is the intensity of interest and g is the log-intensity. Previous work in this area has considered applying regularizers such as the total variation semi-norm to either f or to g := log f. The former is less stable at very low intensity levels and makes selecting tuning parameters challenging. The latter is more amenable to tuning via cross-validation, particularly at low intensity levels, but exhibits numerical instabilities and slow convergence at high intensity levels. This paper describes a novel hybrid approach in which the regularization mode is locally adapted to the signal intensity level. The resulting method yields strong empirical performance relative to previous approaches.