References
- Alpert , N. M. , Chesler , D. A. , Correia , J. A. , Ackerman , R. H. , Chang , J. H. , Finklestein , S. , Davis , S. M. , Brownell , G. L. and Taveras , J. M. 1982 . “Estimation of the Local Statistical Noise in Emission Computed Tomography,” . IEEE Transactions on Medical Imaging , 1 : 142 – 146 .
- Beran , R. , Feuerverger , A. and Hall , P. 1996 . “On Nonparametric Estimation of Intercept and Slope Distributions in Random Coefficient Regression,” . The Annals of Statistics , 6 : 2569 – 2592 .
- Bickel , P. J. and Ritov , Y. 1995 . “Estimating Linear Functionals of a PET Image,” . IEEE Transactions on Medical Imaging , 14 : 81 – 87 .
- Budinger , T. F. , Derenzo , S. E. , Gulberg , G. T. , Greenberg , W. L. and Huesman , R. H. 1978 . “Quantitative Potentials of Dynamic Emission Computed Tomography,” . Journal of Nuclear Medicine , 19 : 309 – 315 .
- Carson , R. E. , Yan , Y. , Daube-Witherspoon , M. E. , Freedman , N. , Bacharach , S. L. and Herscovitch , P. 1993 . “An Approximation Formula for the Variance of PET Region-of-Interest Values,” . IEEE Transactions on Medical Imaging , 12 : 240 – 250 .
- Carroll , R. J. and Hall , P. 1988 . “Optimal Rates of Convergence for Deconvolving a Density,” . Journal of the American Statistical Association , 83 : 1184 – 1186 .
- Fessler , J. A. 1996 . “Mean and Variance of Implicitly Defined Biased Estimators (such as Penalized Maximum Likelihood): Applications to Tomography,” . IEEE Transactions on Image Processing , 5 ( 3 ) : 493 – 506 .
- Fessler , J. A. 1997 . “Approximate Variance Images for Penalized-Likelihood Image Reconstruction,” . Proceedings of the IEEE Nuclear Science Symposium and Medical Imaging Conference , 2 : 949 – 952 .
- Geman , S. and McClure , D. E. “Bayesian Image Analysis: Application to Single Photon Emission Computed Tomography,” . Proceedings of the American Statistical Association Statistical Computing Sections . pp. 12 – 18 .
- Haynor , D. R. and Woods , S. D. 1989 . “Resampling Estimates of Precision in Emission Tomography,” . IEEE Transactions on Medical Imaging , 8 : 337 – 343 .
- Huesman , R. H. 1984 . “A New Fast Algorithm for the Evaluation of Regions of Interest and Statistical Uncertainty in Computed Tomography,” . Physics in Medicine and Biology , 29 : 543 – 552 .
- Johnstone , I. M. and Silverman , B. W. 1990 . “Speed of Estimation in Positron Emission Tomography and Related Inverse Problems,” . The Annals of Statistics , 18 : 251 – 280 .
- Maitra , R. 1996 . “Variability Estimation in Linear Inverse Problems,” , Ph.D. dissertation University of Washington, Dept. of Statistics .
- Mazziotta , J. C. , Phelps , M. E. and Schelbert , H. R. 1986 . Positron Emission Tomography and Autoradiography , New York : Raven .
- Mendelsohn , J. and Rice , J. 1982 . “Deconvolution of Microfluorometric Histograms by B-splines,” . Journal of the American Statistical Association , 77 : 748 – 753 .
- Molina , R. and Ripley , B. D. 1989 . “Using Spatial Models as Priors in Astronomical Image Analysis,” . Applied Statistics , 16 : 193 – 206 .
- Natterer , F. 1986 . Mathematics of Computerized Tomography , New York : Wiley .
- Nychka , D. and Cox , D. D. 1989 . “Convergence Rates for Regularized Solutions of Integral Equations From Discrete Noisy Data,” . The Annals of Statistics , 17 : 556 – 572 .
- Nychka , D. , Wahba , G. , Goldfarb , S. and Pugh , T. 1984 . “Cross-Validated Spline Methods for the Estimation of Three-Dimensional Tumor Size Distributions From Observations on Two-Dimensional Cross-Sections,” . Journal of the American Statistical Association , 79 : 832 – 846 .
- O'Sullivan , F. 1986 . “A Statistical Perspective on Ill-Posed Inverse Problems,” . Statistical Science , 1 : 502 – 527 .
- O'Sullivan , F. 1995 . “A Study of Least Squares and Maximum Likelihood for Image Reconstruction in Positron Emission Tomography,” . The Annals of Statistics , 23 : 1267 – 1300 .
- O'Sullivan , F. and Pawitan , Y. 1996 . “Bandwidth Selection for Indirect Density Estimation Based on Corrupted Histogram Data,” . Journal of the American Statistical Association , 91 : 610 – 627 .
- O'Sullivan , F. , Pawitan , Y. and Haynor , D. 1993 . “Reducing Negativity Artifacts in Emission Tomography: Post-Processing Filtered Backprojection Solutions,” . IEEE Transactions on Medical Imaging , 12 : 653 – 663 .
- Phelps , M. E. , Huang , S. C. , Hoffman , E. J. , Selin , C. , Sokoloff , L. and Kuhl , D. E. 1979 . “Tomographic Measurement of Local Cerebral Glucose Metabolic Rate in Humans With [F-18]2-fluoro-2-deoxy-d-glucose: Validation of Method,” . Annals of Neurology , 6 : 371 – 388 .
- Rosenfeld , A. and Kak , A. C. 1981 . Digital Picture Processing, , 2nd ed. , New York : Academic Press .
- Silverman , B. W. 1986 . “Density Estimation for Statistics and Data Analysis,” , London : Chapman and Hall .
- Silverman , B. W. , Jones , M. C. , Wilson , J. D. and Nychka , D. W. 1990 . “A Smoothed EM Approach to Indirect Estimation Problems, With Particular Reference to Stereology and Emission Tomography,” . Journal of the Royal Statistical Society , 52 : 271 – 324 . Ser. B
- Tanaka , E. and Murayama , H. “Properties of Statistical Noise in Positron Emission Tomography,” . Proceedings of the IEEE International Workshop on Physics and Engineering in Medical Imaging . pp. 158 – 164 .
- Ter-Porgossian , M. M. , Raichle , M. E. and Sobel , B. E. 1980 . “Positron Emission Tomography,” . Scientific American , 243 : 170 – 181 .
- Vardi , Y. and Lee , D. 1993 . “From Image Deblurring to Optimal Investments: Maximum Likelihood Solutions for Positive Linear Inverse Problems,” . Journal of the Royal Statistical Society , 55 : 569 – 599 . Ser. B
- Vardi , Y. , Shepp , L. A. and Kaufman , L. A. 1985 . “Statistical Model for Positron Emission Tomography,” . Journal of the American Statistical Association , 80 : 8 – 37 .
- Wahba , G. 1990 . Spline Models in Statistics , Philadelphia , PA : SIAM .
- Wilson , D. W. and Tsui , B. M. W. 1993 . “Noise Properties of Filtered-Backprojection and ML-EM Reconstructed Emission Tomographic Images,” . IEEE Transactions on Nuclear Sciences , 40 : 1198 – 1203 .
- Zhang , P. 1992 . “On Deconvolution Using Time of Flight Information in Positron Emission Tomography,” . Statistica Sinica , 2 : 553 – 575 .