Performance of the Rayleigh task based on the posterior probability of tomographic reconstructions

The authors seek the best possible performance of the Rayleigh task in which one must decide whether a perceived object is a pair of Gaussian-blurred points or a blurred line. Two Bayesian reconstruction algorithms are used, the first based on a Gaussian prior-probability distribution with a nonnegativity constraint and the second based on an entropic prior. In both cases, the reconstructions that maximize the posterior probability are found. The authors compare the performance of the Rayleigh task obtained with two decision variables, the logarithm of the posterior probability ratio, and the change in the mean-squared deviation from the reconstruction. The evaluation method is based on the results of a numerical testing procedure in which the stated discrimination task is carried out on reconstructions of a randomly generated sequence of images. The ability to perform the Rayleigh task is summarized in terms of a discrimination index that is derived from the area under the receiver operating characteristic curve. The use of the posterior probability does not result in better performance of the Rayleigh task than the mean-squared deviation from the reconstruction.<>