ANALYSIS OF NOISE PROPERTIES OF A CLASS OF EXACT METHODS OF INVERTINGTHE 2-D EXPONENTIAL RADON-TRANSFORM

A general approach that we proposed elsewhere reveals the intrinsic re lationship among methods for inversion of the 2-D exponential Radon tr ansform described by Bellini et al., by Tretiak and Metz, by Hawkins e t al., and by Inouye et al. Moreover, our approach provides an infinit e class of linear methods for inverting the 2-D exponential Radon tran sform. In the work reported here, we systematically investigated the n oise characteristics of the methods in this class, obtaining analytica l forms for the autocovariance and the variance of the images reconstr ucted by use of various methods. The noise properties of a new ''quasi -optimal'' method were then compared theoretically to those of other m ethods of the class. Our analysis demonstrates that the quasi-optimal method achieves smaller global variance in the reconstructed images th an do the other methods of the class. Extensive numerical simulation s tudies confirm this prediction.