According to the imaging process is easily affected by Poisson noise

the image restoration regularization model that fidelity term is described by Kullback-Leibler Euclidean and the regularization term is established by the square root compound function

with adaptive weight coefficients

is proposed.For the gradient degeneration and the large scale Hessian matrix

it is unable to apply the Newton iterative algorithm to the model.In this paper

constraint set is introduced by the magnitude value of degeneration gradient

the diagonal and easily computed Hessian matrix is established

and the improved Newton iterative projection algorithm is proposed.Simulation results show the proposed can effectively restore image

such as the lower relative error and deviation

the higher peak signal to noise ratio

and better visual effect.