中文摘要：

去除医学、天文图像中的泊松噪声一直是人们关注的热点问题之一。在充分分析泊松去噪α-Le模型的基础上结合交替方向乘子（ADMM）算法，给出该模型一基于框式约束的快速求解算法，并证明了该算法的收敛性。数值实验结果表明，该算法在去噪的同时，不仅能很好地保留图像中的边缘及小细节特征，还能大幅提高运算效率。

英文摘要：

The removal problem of Poisson noise in the medical, astronomical images has been one of the hot topics untilnow. In this paper, it firstly analyzes the α -Le model of Poisson noise removal and develops a fast algorithm based on abox constraint to solve numerically the model by incorporating Alternating Direction Multiplier(ADMM) algorithm.Then the convergence of the fast algorithm is proved. Finally, numerical results are reported to show that the proposedalgorithm, at the same time of denoising, not only preserves small detail characteristics in images, but also improves greatlythe computational efficiency.