A new nonlinear filter constructed from the Newton method and EPR in image restoration

The edge-preserving regularization method (EPR) is effective to remove Gaussian noise and impulse noise in image restorations, but till now, we could not say that the problem has been solved very efficiently by state of the art optimization method. In our paper, we will construct a new nonlinear filter from the edge-preserving model and the Newton method, the parameter estimation model in the nonlinear filter will be established, and the solution existence of the model will be proved at the same time. Numerical results demonstrate that the nonlinear filter removes the Gaussian noise from an image as effectively as the edge-preserving regularization method does, and the time for the nonlinear filter to restore an image is less than half time for the edge-preserving regularization method.