9 October 1995 Estimation of smooth integral functionals in emission tomography
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Abstract
We present an algorithm-independent theory of statistical accuracy attainable in emission tomography. Let f denote the tracer density as a function of position (i.e., f is the underlying image). We consider the problem of estimating (Phi) (f) equalsV (integral) (phi) (x)f(x)dx, where (phi) is a smooth function, given n independent observations distributed according to the Radon transform of f. Assuming only that f is bounded above and below away from 0, we construct minimum-variance unbiased (MVU) estimators for (Phi) (f). By definition, the variavnce of the MVU estimator is a best-possible lower bound (depending on (phi) and f) on the variance of unbiased estimators of (Phi) (f). The analysis gives a geometrical explanation of when and by how much estimators based on the standard filtered-backpropagation reconstruction algorithm may be improved.
© (1995) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Alvin Kuruc, "Estimation of smooth integral functionals in emission tomography", Proc. SPIE 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, (9 October 1995); doi: 10.1117/12.224153; https://doi.org/10.1117/12.224153
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