The restoration of blurred image with Poisson noise was studied.According to the statistical maximum a posteriori MAP estimation of the original image,we built a new criterion to measure the fidelity of the estimated image to the original image corrupted by Poisson noise.Because of the ill-posed nature of the image restoration problem,we construct a new variational model with a regularization term.The choice of the edge-preserving regularization function is addressed.To solve the variational model,we transform it to be a nonlinear diffusion equation.An adaptive regularization parameter,which can change its value from a smooth area to an edge area,is proposed.Numerical experiments demonstrate that the proposed method results in high restoration performance.The new model can preserve edges and reduce the Poisson noise effectively.The improved signal to noise ratio(ISNR)is the new model is about 1 dB higher than the traditional iterative regularization method.