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.