Poisson noise commonly occurs in images captured by photon-limited imaging systems such as in astronomy and medicine. As the distribution of Poisson noise depends on the pixel intensity value, noise levels vary from pixels to pixels. Hence, denoising a Poisson-corrupted image while preserving important details can be challenging. In this paper, we propose a Poisson denoising model by incorporating the weighted anisotropic-isotropic total variation (AITV) as a regularization. We then develop an alternating direction method of multipliers with a combination of a proximal operator for an efficient implementation. Lastly, numerical experiments demonstrate that our algorithm outperforms other Poisson denoising methods in terms of image quality and computational efficiency.

翻译：泊松噪声常见于天文学和医学等光子受限成像系统所捕获的图像中。由于泊松噪声的分布依赖于像素强度值，不同像素的噪声水平存在差异。因此，在保留重要细节的同时对受到泊松污染的图像进行去噪是一项具有挑战性的任务。本文通过引入加权各向异性-各向同性全变分（AITV）作为正则化项，提出了一种泊松去噪模型。随后，我们开发了结合近端算子的交替方向乘子法以实现高效求解。最后，数值实验表明，我们的算法在图像质量和计算效率方面优于其他泊松去噪方法。