Poisson Noise Reduction with Higher-order Natural Image Prior Model

Poisson denoising is an essential issue for various imaging applications, such as night vision, medical imaging and microscopy. State-of-the-art approaches are clearly dominated by patch-based non-local methods in recent years. In this paper, we aim to propose a local Poisson denoising model with both structure simplicity and good performance. To this end, we consider a variational modeling to integrate the so-called Fields of Experts (FoE) image prior, that has proven an effective higher-order Markov Random Fields (MRF) model for many classic image restoration problems. We exploit several feasible variational variants for this task. We start with a direct modeling in the original image domain by taking into account the Poisson noise statistics, which performs generally well for the cases of high SNR. However, this strategy encounters problem in cases of low SNR. Then we turn to an alternative modeling strategy by using the Anscombe transform and Gaussian statistics derived data term. We retrain the FoE prior model directly in the transform domain. With the newly trained FoE model, we end up with a local variational model providing strongly competitive results against state-of-the-art non-local approaches, meanwhile bearing the property of simple structure. Furthermore, our proposed model comes along with an additional advantage, that the inference is very efficient as it is well-suited for parallel computation on GPUs. For images of size $512 \times 512$, our GPU implementation takes less than 1 second to produce state-of-the-art Poisson denoising performance.
Comment: 31 pages, 10 figures. To appear in SIAM Journal on Imaging Sciences