[Paper Review] Fast and Accurate Poisson Denoising with Optimized Nonlinear Diffusion

Wensen Feng, Yunjin Chen|arXiv (Cornell University)|Oct 10, 2015

Image and Signal Denoising Methods19 references3 citations

TL;DR

This paper proposes a fast and accurate Poisson denoising method using an optimized trainable nonlinear reaction diffusion (TRDPD) model, which jointly learns linear filters and non-linear influence functions tailored to Poisson noise statistics. The approach achieves state-of-the-art denoising performance in under 0.1 seconds on 512×512 images via efficient GPU-parallelized inference, combining high accuracy with exceptional computational speed.

ABSTRACT

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this study we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly-developed trainable nonlinear reaction diffusion model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with an optimized nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on GPUs. For images of size $512 imes 512$, our GPU implementation takes less than 0.1 seconds to produce state-of-the-art Poisson denoising performance.

Motivation & Objective

• To address the lack of computational efficiency in state-of-the-art Poisson denoising methods, which prioritize accuracy over speed.
• To develop a denoising model that maintains high image restoration quality while achieving extremely low inference time.
• To leverage the trainable nonlinear reaction diffusion framework for Poisson noise, optimizing both filters and influence functions using Poisson statistics.
• To enable efficient parallel computation on GPUs by exploiting the model's simple, convolutional structure.
• To provide a practical solution for real-time applications in medical imaging, microscopy, and night vision where both speed and accuracy are critical.

Proposed method

• The method formulates a trainable nonlinear reaction diffusion model as a recurrent convolutional network with learned activation functions, replacing standard fixed activations.
• It derives an energy functional based on Poisson noise distribution and optimizes the model parameters (filters and influence functions) via end-to-end training.
• The influence functions are learned as nonlinear, adaptive functions that control diffusion strength based on local image gradients and intensity.
• The model uses a small number of explicit diffusion steps, enabling fast inference and high parallelism suitable for GPU acceleration.
• The training process explicitly accounts for signal-dependent Poisson noise, avoiding variance-stabilizing transforms that degrade performance at low intensities.
• The final model is implemented as a lightweight, differentiable architecture that performs denoising through iterative, spatially adaptive diffusion.

Experimental results

Research questions

• RQ1 Can a trainable nonlinear diffusion model be effectively optimized for Poisson denoising to achieve both high accuracy and low computational cost?
• RQ2 How does the performance of a diffusion model trained with Poisson-specific statistics compare to state-of-the-art methods in terms of PSNR and SSIM?
• RQ3 To what extent can the model’s simple structure and convolutional operations enable efficient GPU parallelization for real-time inference?
• RQ4 Does avoiding variance-stabilizing transforms (e.g., Anscombe) lead to better performance at low signal intensities compared to VST-based methods?
• RQ5 Can joint optimization of filters and influence functions in a diffusion framework surpass standard CNNs with fixed activation functions in denoising quality?

Key findings

• For 512×512 images with peak intensity 4, the GPU-optimized TRDPD model achieves inference in less than 0.1 seconds, significantly outperforming CPU-based competitors.
• On the standard test set, TRDPD with 7×7 filters achieves a PSNR of 29.06 and SSIM of 0.809 on Image 8 (peak=40), outperforming BM3D and NLSPCA.
• The TRDPD model achieves a PSNR of 27.01 and SSIM of 0.856 on Image 7 (peak=20), surpassing BM3D and NLSPCA in both metrics.
• The model's performance is consistently superior to BM3D and NLSPCA across all test images and noise levels, especially in low-peak regimes where VST-based methods fail.
• The TRDPD model demonstrates strong generalization across diverse image types and noise levels, maintaining high accuracy without requiring image-specific tuning.
• The model’s simple, convolutional structure enables efficient GPU parallelization, making it suitable for real-time applications in medical and scientific imaging.