Analysis of noise properties of a class of exact methods of inverting the 2-D exponential radon transform [SPECT application]

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Abstract
A general approach that the authors proposed elsewhere reveals the intrinsic relationship among methods for inversion of the 2-D exponential Radon transform described by Bellini et al. (1979), by Tretiak and Metz (1980), by Hawkins et al. (1988), and by Inouye et al. (1989). Moreover, the authors' approach provides an infinite class of linear methods for inverting the 2-D exponential Radon transform. In the work reported here, the authors systematically investigated the noise characteristics of the methods in this class, obtaining analytical forms for the autocovariance and the variance of the images reconstructed by use of various methods. The noise properties of a new "quasi-optimal" method were then compared theoretically to those of other methods of the class. The authors' analysis demonstrates that the quasi-optimal method achieves smaller global variance in the reconstructed images than do the other methods of the class. Extensive numerical simulation studies confirm this prediction.