In medical computed tomography (CT) the tomographic images are reconstructed from planar information collected 180∘ to 360∘ around the patient. In clinical applications, the reconstructions are typically produced using a filtered backprojection algorithm. Filtered backprojection methods have limitations that create a high percentage of statistical uncertainty in the reconstructed images. Many techniques have been developed which produce better reconstructions, but they tend to be computationally expensive, and thus, impractical for clinical use;Artificial neural networks (ANN) have been shown to be adept at learning and then simulating complex functional relationships. For medical tomography, a neural network can be trained to produce a reconstructed medical image given the planar data as input. Once trained an ANN can produce an accurate reconstruction very quickly;A backpropagation ANN with statistically derived activation functions has been developed to improve the trainability and generalization ability of a network to produce accurate reconstructions. The tailored activation functions are derived from the estimated probability density functions (p.d.f.s) of the ANN training data set. A set of sigmoid derivative functions are fitted to the p.d.f.s and then integrated to produce the ANN activation functions, which are also estimates of the cumulative distribution functions (c.d.f.s) of the training data. The statistically tailored activation functions and their derivatives are substituted for the logistic function and its derivative that are typically used in backpropagation ANNs;A set of geometric images was derived for training an ANN for cardiac SPECT image reconstruction. The planar projections for the geometric images were simulated using the Monte Carlo method to produce sixty-four 64-quadrant planar views taken 180 about each image. A 4096 x 629 x 4096 architecture ANN was simulated on the MasPar MP-2, a massively parallel single-instruction multiple-data (SIMD) computer. The ANN was trained on the set of geometric tomographic images. Trained on the geometric images, the ANN was able to generalize the input-to-output function of the planar data-to-tomogram and accurately reconstruct actual cardiac SPECT images.