Estimation of smooth integral functionals in emission tomography

Alvin Kuruc

doi:10.1117/12.224153

9 October 1995 Estimation of smooth integral functionals in emission tomography

Alvin Kuruc

Proceedings Volume 2570, Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications; (1995) https://doi.org/10.1117/12.224153
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

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.

Citation Download Citation

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); https://doi.org/10.1117/12.224153

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