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In this work, we derive explicit relationships between an ideal sinogram in 2D SPECT and the sinogram after degradation by constant attenuation and by distance-dependent spatial resolution that is described by either a Cauchy or a Gaussian function. Attempts to reduce statistical variance in the reconstructed image lead to the development of infinite classes of closed-form methods for estimation of the ideal sinogram, We applied this approach to 2D SPECT in both computer-simulation and real-data studies. Extensive computer-simulation studies demonstrate that the counterparts of a 'quasi-optimal' method, which we had proved to be the optimal member of its class in 2D SPECT when only attenuation is present, provide the smallest global image variance among the methods in their classes also when Cauchy or Gaussian functions describe the distance-dependent spatial resolution function.

We compare two methods of training artificial neural networks (ANNs) that potentially reduce the risk of the neural network overfitting the training data set. We refer to these methods as training with jitter. In one method of training with jitter, a new random noise vector is added to each training-data vector between successive iterations. In this work, we propose a different method of training with jitter, in which instead of adding different random noise vectors between iterations, a number of random vectors are used to expand the training data set prior to training. This artificially expanded data set is then used to train the artificial neural network in the conventional manner. These two methods are compared to the conventional method of training artificial neural networks. We find that although training with a single expanded training data set does increase the performance of the neural networks, overfitting can still occur after a large number of training iterations. [Copyright &y& Elsevier]