A method for approximating the density of maximum-likelihood and maximum a posteriori estimates under a Gaussian noise model

Barndorff-Nielsen, 1983, On a formula for the distribution of the maximum likelihood estimator, Biometrika, 70, 343, 10.1093/biomet/70.2.343 Barrett, 1990, Objective assessment of image quality: effects of quantum noise and object variability, J. Opt. Soc. Am. A, 7, 1266, 10.1364/JOSAA.7.001266 Barrett, 1981, 1, 88 Fessler, 1995, Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): applications to tomography, IEEE Trans. Image Process., 5, 493, 10.1109/83.491322 Fessler, 1993, Cramér-Rao lower bounds for biased image reconstruction, Proc. Midwest Symp. on Circuits and Systems, 1, 253, 10.1109/MWSCAS.1993.343082 Geman, 1984, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Trans. PAMI, 6, 721, 10.1109/TPAMI.1984.4767596 Mardia, 1979 Müller, 1990, Maximum-likelihood estimation: a mathematical model for quantitation in nuclear medicine, J. Nucl. Med., 31, 1693 Müller, 1995, Estimation performance at low SNR: predictions of the Barankin bound, 2432, 157 Müller, 1995, The efficiency of ML-estimation at low SNR can be inferred from the probability distribution of the estimates, J. Nucl. Med., 36, 119 Press, 1992, 412 Van Trees, 1968