Poisson noise removal of images on graphs using tight wavelet frames

After many years of study, the subject of image denoising on the flat domain is well developed. However, many practical problems arising from different areas, such as computer vision, computer graphics, geometric modeling and medical imaging, involve images on the irregular domain sets such as graphs. In this paper, we consider Poisson and mixed Poisson–Gaussian noise removal of images on graphs. Based on the statistical characteristic of the observed noisy images, we propose a wavelet frame-based variational model to restore images on graphs. The model contains a weighted ℓ 2 fidelity term and an ℓ 1 -regularized term which makes additional use of the tight wavelet frame transform on graphs in order to preserve key features such as textures and edges of images. We then apply the popular alternating direction method of multipliers (ADMM) to solve the model. Finally, we provide supporting numerical experiments on graphs and compare with other denoising methods. The results on some image denoising tasks indicate the effectiveness of our method.