A weighted least-squares method for PET

In this paper, the authors present a reconstruction algorithm for positron emission tomography that minimizes a weighted least-squares (WLS) objective function. The weights are based on the covariance matrix of the model error and depend on the unknown parameters. The algorithm guarantees nonnegative estimates, and in simulation studies it converged faster and had significantly better resolution and contrast than the ML-EM algorithm. Although simulations suggest that the proposed algorithm is globally convergent, a proof of convergence has not been found yet. Nevertheless, the authors are able to show that it produces estimates that decrease the objective function monotonically with increasing iterations.