Estimation of linear functionals in emission tomography
Abstract
In emission tomography, the spatial distribution of a radioactive tracer is estimated from a finite sample of externally-detected photons. We present an algorithm-independent theory of statistical accuracy attainable in emission tomography that makes minimal assumptions about the underlying image. Let f denote the tracer density as a function of position (i.e., f is the image being estimated). We consider the problem of estimating the linear functional {Phi}(f) {triple_bond} {integral}{phi}(x)f(x) dx, where {phi} is a smooth function, from n independent observations identically distributed according to the Radon transform of f. Assuming only that f is bounded above and below away from 0, we construct statistically efficient estimators for {Phi}(f). By definition, the variance of the efficient estimator is a best-possible lower bound (depending on and f) on the variance of unbiased estimators of {Phi}(f). Our results show that, in general, the efficient estimator will have a smaller variance than the standard estimator based on the filtered-backprojection reconstruction algorithm. The improvement in performance is obtained by exploiting the range properties of the Radon transform.
- Authors:
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE, Washington, DC (United States); Department of Health and Human Services, Washington, DC (United States)
- OSTI Identifier:
- 110711
- Report Number(s):
- LBL-37032-Rev.
ON: DE96000876; TRN: 95:007312
- DOE Contract Number:
- AC03-76SF00098
- Resource Type:
- Technical Report
- Resource Relation:
- Other Information: PBD: Aug 1995
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 44 INSTRUMENTATION, INCLUDING NUCLEAR AND PARTICLE DETECTORS; EMISSION COMPUTED TOMOGRAPHY; ACCURACY; MATHEMATICAL MODELS; DATA COVARIANCES; PARAMETRIC ANALYSIS; FUNCTIONAL ANALYSIS; STATISTICAL MODELS
Citation Formats
Kuruc, A. Estimation of linear functionals in emission tomography. United States: N. p., 1995.
Web. doi:10.2172/110711.
Kuruc, A. Estimation of linear functionals in emission tomography. United States. https://doi.org/10.2172/110711
Kuruc, A. 1995.
"Estimation of linear functionals in emission tomography". United States. https://doi.org/10.2172/110711. https://www.osti.gov/servlets/purl/110711.
@article{osti_110711,
title = {Estimation of linear functionals in emission tomography},
author = {Kuruc, A},
abstractNote = {In emission tomography, the spatial distribution of a radioactive tracer is estimated from a finite sample of externally-detected photons. We present an algorithm-independent theory of statistical accuracy attainable in emission tomography that makes minimal assumptions about the underlying image. Let f denote the tracer density as a function of position (i.e., f is the image being estimated). We consider the problem of estimating the linear functional {Phi}(f) {triple_bond} {integral}{phi}(x)f(x) dx, where {phi} is a smooth function, from n independent observations identically distributed according to the Radon transform of f. Assuming only that f is bounded above and below away from 0, we construct statistically efficient estimators for {Phi}(f). By definition, the variance of the efficient estimator is a best-possible lower bound (depending on and f) on the variance of unbiased estimators of {Phi}(f). Our results show that, in general, the efficient estimator will have a smaller variance than the standard estimator based on the filtered-backprojection reconstruction algorithm. The improvement in performance is obtained by exploiting the range properties of the Radon transform.},
doi = {10.2172/110711},
url = {https://www.osti.gov/biblio/110711},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Aug 01 00:00:00 EDT 1995},
month = {Tue Aug 01 00:00:00 EDT 1995}
}