We evaluate several tomographic reconstruction algorithms on the basis of how well one can perform the Rayleigh discrimination task using the reconstructed images. The Rayleigh task is defined here as deciding whether a perceived object is either a pair of neighboring points or a line, both convolved with a 2D Gaussian. The method of evaluation 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 discriminability index that is derived from the area under the receiver-operating characteristic (ROC) curve. Reconstruction algorithms employing a nonnegativity constraint are compared, including maximum a posteriori (MAP) estimation based on the Bayesian method with entropy and Gaussian priors as well as the additive and multiplicative versions of the algebraic reconstruction technique (ART and MART). The performance of all four algorithms tested is found to be similar for complete noisy data. However, for sparse noiseless data, the MAP algorithm based on the Gaussian prior does not perform as well as the others.
Keywords: receiver-operating characteristic, Rayleigh task, observer performance, evaluation of image quality
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