A method and apparatus is provided to iteratively reconstruct a PET image for emission data using separable quadratic surrogates (SQS). The quadratic surrogates include a Poisson likelihood surrogate that has a curvature that depends on a back-projection of an inverse of mean-background signal. The method can be used with Nesterov acceleration and ordered subsets to achieve quadratic convergence to an image minimizing a Poisson Likelihood objective function that includes a regularizer that penalizes roughness in the reconstructed image.
