Blind Restoration of Poisson Images Using Adaptive Euler's Elastica Regularization

In a wide range of applications such as astronomy, biology, and medical imaging, acquired data are often corrupted by Poisson noise and blurring artifacts. Poisson noise is difficult to eliminate due to its signal-dependent and multiplicative properties. In this paper, a new adaptive Euler's elastica regularization model for blind restoration of Poisson images is proposed. This model combines the advantages of an adaptive weighted matrix and Euler's elastica regularization, which can mitigate the staircase effects while effectively preserving the local features of the image. In addition, an efficient alternating direction method of multipliers (ADMM) for solving this nonconvex model is designed. A large number of experiments are carried out on natural and synthetic images, respectively. The related results show that the proposed method can not only obtain a more accurate blur kernel but also improve the quality of the recovered image significantly.