中文摘要：

利用泊松噪声分布与图像灰度值相关这一特性,结合图像的水平集曲线对图像灰度值的刻画能力,在Bayesian-MAP框架下,提出了欧拉弹性正则与泊松似然保真的图像泊松去噪变分正则化模型.利用交替方向乘子法,将原问题转化为几个不同低阶子问题的求解.对于子问题中出现的高阶非线性项,利用滞后扩散不动点迭代进行线性化,从而得到模型的快速迭代求解算法.通过数值模拟实验,证明了当图像受不同强度泊松噪声影响时,所提出的泊松去噪方法都能够有效的抑制泊松噪声,同时具有良好的结构保持性能.

英文摘要：

Poisson noise has strong relationship with the gray-values of image,meanwhile the gray-values of image can be represented by level line. In the framework of the Bayesian-MAP,a Poisson denoising variational regularization model is proposed. The Euler＇s elastica energy is used as a prior regularization term combined with negative-log Poisson likelihood.By using the alternating direction method of multipliers（ ADMM）,we transform the original high-order optimization problem into several low-order sub-problems. Then the lagged diffusivity fixed point iteration is applied to solve the high-order nonlinear term. For images with strong or weak Poisson noise,experiments showthe validity and efficiency of the proposed method both in preserving geometric structure and suppressing noise.