基于Shearlet变换的泊松噪声图像复原问题研究

为了解决泊松噪声图像的复原问题，几种正则化方法已被提出，其中最著名的是全变差（TV）模型，但TV模型会引起阶梯效应。总广义变差（TGV）是全变差的推广，用TGV作为正则项来恢复泊松图像，可以消除阶梯效应，但图像的边缘细节信息不能很好地保持。为了克服这个缺点，基于TGV和Shearlet变换，该文提出了一种新的正则化模型，并用交替方向乘子法（ADMM）求解。数值结果有效地展示了该模型在保持图像边缘细节上的优越性。

Research on Poisson Noise Image Restoration Problems Based on Shearlet Transform

Restoring Poisson noise images has been drawn a lot of attention in recent years. To solve this problem, several regularization methods have been put forward. One of the most famous methods is the Total variation (TV) model. However, the TV model will cause staircasing effects. The total generalized variation (TGV) is the extension of TV. Using TGV as a regularization term to recover the Poission image can eliminate staircase effects but the edge details will not preserved very well. In order to overcome this drawback, based on TGV and Shearlet transform, we propose a new regularization method. The proposed model is solved by the alternating direction method of multiplier (ADMM). The numerical results reflect the efficiency of the new model in dealing with Poisson noise image.