Cited by 863Medical Imaging Techniques and ApplicationsNumerical methods in inverse problemsImage and Signal Denoising Methods

The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.

A Statistical Model for Positron Emission Tomography

Vardi, Y., Shepp, L. A., Kaufman, L.·1985·Journal of the American Statistical Association

DOI 10.1080/01621459.1985.10477119

Open this paper in CoChat — free account

Abstract

Positron emission tomography (PET)—still in its research stages—is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner. Much as in X-ray transmission tomography and other modes of computerized tomography, the quality of the reconstructed image in PET is very sensitive to the mathematical algorithm to be used for reconstruction. In this article, we tailor a mathematical model to the physics of positron emissions, and we use the model to describe the basic image reconstruction problem of PET as a standard problem in statistical estimation from incomplete data. We describe various estimation procedures, such as the maximum likelihood (ML) method (using the EM algorithm), the method of moments, and the least squares method. A computer simulation of a PET experiment is then used to demonstrate the ML and the least squares reconstructions. The main purposes of this article are to report on what we believe is an important contribution of statistics to PET and to familiarize statisticians with this exciting field that can benefit from further statistical methodologies to be developed with PET problems in mind. Thus no background in physics or previous knowledge of computerized tomography is assumed. The emphasis is on the basic PET model and the statistical methodology needed for it.

Integrity signals

Registry

Crossref · 10.1080/01621459.1985.10477119

Cites

28 of 28 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Maximum Likelihood from Incomplete Data Via the EM Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444
Linear Statistical Inference and its Applications
Rao, C. R. (1973) · Wiley series in probability and statistics · doi:10.1002/9780470316436 · Cited by 10,474
Iterative Solution of Nonlinear Equations in Several Variables
Ortega, J. M., & Rheinboldt, W. C. (2000) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898719468 · Cited by 6,919
Journal of The American Statistical Association
Fienberg, S. E. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess1317 · Cited by 6,289
Maximum likelihood estimation from incomplete data via the EM algorithm
Dempster, A. P. (1977) · Journal of the Royal Statistical Society Series A (Statistics in Society) · Cited by 4,543
Maximum Likelihood Reconstruction for Emission Tomography
Shepp, L. A., & Vardi, Y. (1982) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.1982.4307558 · Cited by 4,429
Self-citation
The Fourier reconstruction of a head section
Shepp, L. A., & Logan, B. F. (1974) · IEEE Transactions on Nuclear Science · doi:10.1109/tns.1974.6499235 · Cited by 2,202
Self-citation
EM reconstruction algorithms for emission and transmission tomography.
Lange, K. L., & Carson, R. E. (1984) · PubMed · Cited by 1,775
Nonlinear Programming: A Unified Approach.
Beale, E. M. L., & Zangwill, W. I. (1970) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2343701 · Cited by 1,059
Nonlinear Programming: A Unified Approach
Peterson, D. W., & Zangwill, W. I. (1972) · Econometrica · doi:10.2307/1909424 · Cited by 1,011

Show all 27 references

Research works printed but not linked: 2

Lakshminarayanan , A. V. 1975 . “Reconstruction From Divergent Ray Data,” , State University of New York at Buffalo, Computer Science Dept. . Technical Report No. 92
Peng , J. C. M. 1975 . “Simultaneous Estimation of the Parameters of Independent Poisson Distributions,” , Stanford University, Dept. of Statistics . Technical Report No. 78

Sorted by citations

Items 301–400 of 861

A smoothed em algorithm for the solution of wicksell's corpuscle problem
Wilson, J. D. (1989) · Journal of Statistical Computation and Simulation · doi:10.1080/00949658908811144 · Cited by 17
Application of image restoration methods for confocal fluorescence microscopy
van Kempen, G. M. P., A, L. J. V. V., & Verveer, P. J. (1997) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.271257 · Cited by 17
Optimal Measurement Conditions for Spatiotemporal Eeg/Meg Source Analysis
Huizenga, H. M., Heslenfeld, D. J., & Molenaar, P. C. M. (2002) · Psychometrika · doi:10.1007/bf02294848 · Cited by 17
Filter for biomedical imaging and image processing
Mondal, P. P., Rajan, K., & Ahmad, I. (2006) · Journal of the Optical Society of America A · doi:10.1364/josaa.23.001678 · Cited by 16
Maximum-likelihood absorption tomography
Řeháček, J., Hradil, Z., Zawisky, M., Treimer, W., & Ströbl, M. (2002) · Europhysics Letters (EPL) · doi:10.1209/epl/i2002-00181-4 · Cited by 16
Overcoming the Multiplex Disadvantage by Using Maximum-Likelihood Inversion
Bialkowski, S. E. (1998) · Applied Spectroscopy · doi:10.1366/0003702981943923 · Cited by 16
Object Dependency of Resolution in Reconstruction Algorithms With Interiteration Filtering Applied to PET Data
Mustafovic, S., & Thielemans, K. (2004) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2004.824225 · Cited by 16
Iterative Reconstruction Algorithms Based on Cross-Entropy Minimization
Byrne, C. L. (1996) · The IMA volumes in mathematics and its applications · doi:10.1007/978-1-4612-4056-3_1 · Cited by 16
Object dependency of resolution and convergence rate in OSEM with filtering
Mustafovic, S., Thielemans, K., Hogg, D. W., & Bloomfield, P. (2005) · IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) · doi:10.1109/nssmic.2001.1008689 · Cited by 16
On photon correlation measurements of colloidal size distributions using Bayesian strategies
Iqbal, M. (2000) · Journal of Computational and Applied Mathematics · doi:10.1016/s0377-0427(99)00341-6 · Cited by 16
Application of deconvolution methods to gamma-radiation spectra of thermonuclear plasma
Khilkevitch, E., Shevelev, A., Chugunov, I. N., Naidenov, V. O., Gin, D. B., & Doinikov, D. N. (2013) · Technical Physics Letters · doi:10.1134/s1063785013010161 · Cited by 16
Increased depth of field and stereo pairs of fluorescence micrographs via inverse filtering and maximum‐likelihood estimation
Holmes, T. J., Liu, Y., Khosla, D., & Agard, D. A. (1991) · Journal of Microscopy · doi:10.1111/j.1365-2818.1991.tb03209.x · Cited by 16
Assessing quantification for the EMS algorithm
Latham, G. A., & Anderssen, R. (1994) · Linear Algebra and its Applications · doi:10.1016/0024-3795(94)90467-7 · Cited by 16
A Region-Based Segmentation Method for Multichannel Image Data
Bose, S., & O’Sullivan, F. (1997) · Journal of the American Statistical Association · doi:10.1080/01621459.1997.10473606 · Cited by 16
The MM Algorithm
Lange, K. L. (2012) · Springer texts in statistics · doi:10.1007/978-1-4614-5838-8_8 · Cited by 15
Stochastic EM methods with variance reduction for penalised PET reconstructions
Kereta, Ž., Twyman, R., Arridge, S., Thielemans, K., & Jin, B. (2021) · Inverse Problems · doi:10.1088/1361-6420/ac2d74 · Cited by 15
Learned Primal Dual Reconstruction for PET
Guazzo, A., & Colarieti-Tosti, M. (2021) · Journal of Imaging · doi:10.3390/jimaging7120248 · Cited by 15
Monotonically Overrelaxed EM Algorithms
Yu, Y. (2012) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2012.672115 · Cited by 15
Local-EM and the EMS Algorithm
Fan, C. S., Stafford, J. E., & Brown, P. E. (2011) · Journal of Computational and Graphical Statistics · doi:10.1198/jcgs.2011.10106 · Cited by 15
Non-negatively constrained image deblurring with an inexact interior point method
Bonettini, S., & Serafini, T. (2009) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2009.02.020 · Cited by 15
Iterative algorithms for unmixing of hyperspectral imagery
Vélez-Reyes, M., Puetz, A. M., Hoke, M. P., Lockwood, R. B., & Rosario, S. (2003) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.497802 · Cited by 15
Using wavelet methods to solve noisy Abel-type equations with discontinuous inputs
Hall, P. A., Paige, R. L., & Ruymgaart, F. H. (2003) · Journal of Multivariate Analysis · doi:10.1016/s0047-259x(02)00043-x · Cited by 15
Image reconstruction for a multi-layer Compton telescope: an analytical model for three interaction events
Röser, J., Muñoz, E., Barrientos, L., Barrio, J., Bernabéu, J., Borja-Lloret, M., Etxebeste, A., Llosa, G., Ros, A., Viegas, R., et al. (2020) · Physics in Medicine and Biology · doi:10.1088/1361-6560/ab8cd4 · Cited by 15
Image restoration and reconstruction with a Bayesian approach
Kao, C.-M., Pan, X., Chen, C.-T., & Wong, W. H. (1998) · Medical Physics · doi:10.1118/1.598241 · Cited by 15
Deconvolution of Sparse Positive Spikes
Li, L. M., & Speed, T. P. (2004) · Journal of Computational and Graphical Statistics · doi:10.1198/106186004x13118 · Cited by 15
Multiresolution Genetic Algorithms and Markov chain Monte Carlo
Holloman, C. H., Lee, H. K. H., & Higdon, D. (2006) · Journal of Computational and Graphical Statistics · doi:10.1198/106186006x157423 · Cited by 15
Positron emission tomography, Borel measures and weak convergence
Mair, B. A., Rao, M., & Anderson, J. M. M. (1996) · Inverse Problems · doi:10.1088/0266-5611/12/6/011 · Cited by 15
Stationary Positron Emission Tomography and Its Image Reconstruction
Tanaka, E., Nohara, N., Tomitani, T., Yamamoto, M., & Murayama, H. (1986) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.1986.4307778 · Cited by 15
High-Performance Statistical Computing in the Computing Environments of the 2020s
Ko, S., Zhou, H., Zhou, J. J., & Won, J. (2022) · Statistical Science · doi:10.1214/21-sts835 · Cited by 13
Calibration of neutron spectrometers based on a BC-501A liquid scintillator using the neutron–gamma coincidence method
Iliasova, M., Shevelev, A., Khilkevitch, E., Chugunov, I. N., Минаев, В. Б., Gin, D. B., Doinikov, D. N., Polunovsky, I. A., Naidenov, V. O., Kozlovskiy, M. A., et al. (2020) · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment · doi:10.1016/j.nima.2020.164590 · Cited by 14
Iterative regularization algorithms for constrained image deblurring on graphics processors
Ruggiero, V., Serafini, T., Zanella, R., & Zanni, L. (2010) · Journal of Global Optimization · doi:10.1007/s10898-009-9516-x · Cited by 14
Large Scale Inverse Problems
Cullen, M., Freitag, M. A., Kindermann, S., & Scheichl, R. (2013) · De Gruyter eBooks · doi:10.1515/9783110282269 · Cited by 14
A new smoothing-regularization approach for a maximum-likelihood estimation problem
Iusem, A. N., & Svaiter, B. F. (1994) · Applied Mathematics & Optimization · doi:10.1007/bf01189476 · Cited by 14
On the stabilization inherent in the EMS algorithm
Latham, G. A., & Anderssen, R. (1994) · Inverse Problems · doi:10.1088/0266-5611/10/1/013 · Cited by 14
Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes
Hudson, H. M., & Ma, J. (1994) · Statistical Methods in Medical Research · doi:10.1177/096228029400300104 · Cited by 14
Cross-reference weighted least square estimates for positron emission tomography
Lu, H., Chen, C., & Yang, I.-H. (1998) · IEEE Transactions on Medical Imaging · doi:10.1109/42.668690 · Cited by 14
Statistical models of a priori information for image processing: neighboring correlation constraints
Liang, Z. (1988) · Journal of the Optical Society of America A · doi:10.1364/josaa.5.002026 · Cited by 14
Neural Networks and the BiadVariance Dilemma
Geman, S., & Bienenstock, E. (1992) · Cited by 14
The impact of automatic tube current modulation related settings of a modern GE CT scanner on image quality and patient dose; details do matter
Tsalafoutas, I. A., AlKhazzam, S., & Kharita, M. H. (2024) · Journal of Applied Clinical Medical Physics · doi:10.1002/acm2.14356 · Cited by 13
Maximum-likelihood x-ray computed-tomography finite-beamwidth considerations
Browne, J. A., Boone, J. M., & Holmes, T. J. (1995) · Applied Optics · doi:10.1364/ao.34.005199 · Cited by 13
State estimation in quantum homodyne tomography with noisy data
Aubry, J.-M., Butucea, C., & Méziani, K. (2008) · Inverse Problems · doi:10.1088/0266-5611/25/1/015003 · Cited by 13
Intraoperative detection of 18F-FDG-avid tissue sites using the increased probe counting efficiency of the K-alpha probe design and variance-based statistical analysis with the three-sigma criteria
Povoski, S. P., Chapman, G., Murrey, D. A., Lee, R., Martin, E. W., & Hall, N. C. (2013) · BMC Cancer · doi:10.1186/1471-2407-13-98 · Cited by 13
Regularization of Ill-Posed Problems with Non-negative Solutions
Clason, C., Kaltenbacher, B., & Resmerita, E. (2019) · Springer eBooks · doi:10.1007/978-3-030-25939-6_5 · Cited by 13
Muon Tomography Algorithms for Nuclear Threat Detection
Hoch, R., Mitra, D., Gnanvo, K., & Hohlmann, M. (2009) · Studies in computational intelligence · doi:10.1007/978-3-540-92814-0_35 · Cited by 13
Ringing reduction in image restoration algorithms using a constraint on the inferior bound of the solution
Lantéri, H., Roche, M., Gaucherel, P., & Aime, C. J. (2002) · Signal Processing · doi:10.1016/s0165-1684(02)00336-5 · Cited by 13
Limited-memory scaled gradient projection methods for real-time image deconvolution in microscopy
Porta, F., Zanella, R., Zanghirati, G., & Zanni, L. (2014) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2014.08.035 · Cited by 13
EMPIRICAL STUDIES OF CROSS-REFERENCE MAXIMUM LIKELIHOOD ESTIMATE RECONSTRUCTION FOR POSITRON EMISSION TOMOGRAPHY
Tu, K.-Y., Chen, T., Lu, H. H., Liu, R.-S., CHOU, K. L., Chen, C., & Chen, J. (2001) · Biomedical Engineering Applications Basis and Communications · doi:10.4015/s1016237201000029 · Cited by 13
Selection of projection set and the order of calculation in ordered subsets expectation maximization method
Takahashi, M., & Ogawa, K. (2002) · IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) · doi:10.1109/nssmic.1997.670584 · Cited by 13
Acceleration of maximum likelihood reconstruction, using frequency amplification and attenuation compensation
Nuyts, J. L., Suetens, P., & Mortelmans, L. (1993) · IEEE Transactions on Medical Imaging · doi:10.1109/42.251114 · Cited by 13
Quadratic Growth Conditions and Uniqueness of Optimal Solution to Lasso
Bello-Cruz, Y., Li, G., & Nghia, T. T. A. (2022) · Journal of Optimization Theory and Applications · doi:10.1007/s10957-022-02013-2 · Cited by 12
Adaptive total variation regularization based scheme for Poisson noise removal
Zhou, W., & Li, Q. (2012) · Mathematical Methods in the Applied Sciences · doi:10.1002/mma.2587 · Cited by 12
Spatial Auto-Regressive Analysis of Correlation in 3-D PET With Application to Model-Based Simulation of Data
Huang, J., Mou, T., O'Regan, K. N., & O’Sullivan, F. (2019) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2019.2938411 · Cited by 12
A neural network with encoded visible edge prior for limited‐angle computed tomography reconstruction
Ma, G., Zhang, Y., Zhao, X., Wang, T., & Li, H. (2021) · Medical Physics · doi:10.1002/mp.15205 · Cited by 12
An algorithm for the generation of silicon nitride structures
Wippler, J., & Böhlke, T. (2011) · Journal of the European Ceramic Society · doi:10.1016/j.jeurceramsoc.2011.10.001 · Cited by 12
Poisson Noise Removal Scheme Based on Fourth‐Order PDE by Alternating Minimization Algorithm
Zhou, W., & Li, Q. (2012) · Abstract and Applied Analysis · doi:10.1155/2012/965281 · Cited by 12
An improved ems algorithm for back-projection of aids incidence data
Marschner, I. C., & Watson, L. F. (1994) · Journal of Statistical Computation and Simulation · doi:10.1080/00949659408811595 · Cited by 12
Camouflaged Deconvolution With Application to Blood Curve Modeling in FDG PET Studies
Olshen, A. B., & O’Sullivan, F. (1997) · Journal of the American Statistical Association · doi:10.1080/01621459.1997.10473650 · Cited by 12
Fuzzy-rule-based image reconstruction for positron emission tomography
Mondal, P. P., & Rajan, K. (2005) · Journal of the Optical Society of America A · doi:10.1364/josaa.22.001763 · Cited by 12
Bandwidth Selection for Indirect Density Estimation Based on Corrupted Histogram Data
O’Sullivan, F., & Yudi Pawitan, Y. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476930 · Cited by 12
ON EM-LIKE ALGORITHMS FOR MINIMUM DISTANCE ESTIMATION
Eggermont, P. P. B., & LaRiccia, V. N. (1998) · Cited by 12
Expectation propagation for Poisson data
Zhang, C. B. C., Arridge, S., & Jin, B. (2019) · Inverse Problems · doi:10.1088/1361-6420/ab15a3 · Cited by 12
Analysis and Reconstruction of Medical Images Using Prior Information
Johnson, V. E., Bowsher, J. E., Jaszczak, R. J., & Turkington, T. G. (1995) · Lecture notes in statistics · doi:10.1007/978-1-4612-2546-1_4 · Cited by 12
A Cheaper Way to Compute Generalized Cross-Validation as a Stopping Rule for Linear Stationary Iterative Methods
Santos, R. J., & Pierro, Á. R. D. (2003) · Journal of Computational and Graphical Statistics · doi:10.1198/1061860031815 · Cited by 12
An Analysis of the Role of Positivity and Mixture Model Constraints in Poisson Deconvolution Problems
O’Sullivan, F., & Choudhury, K. R. (2001) · Journal of Computational and Graphical Statistics · doi:10.1198/106186001317243395 · Cited by 12
Squared polynomial extrapolation methods with cycling: an application to the positron emission tomography problem
Roland, C., Varadhan, R., & Frangakis, C. (2007) · Numerical Algorithms · doi:10.1007/s11075-007-9094-2 · Cited by 12
Maximum penalized likelihood estimation and smoothed em algorithms for positive integral equatioins of the first kind
Eggermont, P. P. B., & LaRiccia, V. N. (1996) · Numerical Functional Analysis and Optimization · doi:10.1080/01630569608816722 · Cited by 12
Estimating Precision in Functional Images
Maitra, R. (1997) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.1997.10474732 · Cited by 12
Statistics in Psychiatry
Everitt, B. J. (1987) · Statistical Science · doi:10.1214/ss/1177013333 · Cited by 12
Study of the convergence properties of the EM algorithm-a new stopping rule
Kontaxakis, G., & Tzanakos, G. (2003) · IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) · doi:10.1109/nssmic.1992.301047 · Cited by 12
Data Augmentation Schemes Applied to Image Restoration
Johnson, V. E., Wong, W. H., Hu, X. P., & Chen, C.-T. (1992) · Springer eBooks · doi:10.1007/978-3-642-77888-9_14 · Cited by 12
A framework for incorporating structural prior information into the estimation of medical images
Johnson, V. E. (2005) · Springer eBooks · doi:10.1007/bfb0013796 · Cited by 12
The design of an animal PET: flexible geometry for achieving optimal spatial resolution or high sensitivity
Weber, S., Terstegge, A., Halling, H., Herzog, H. R., Reinartz, R., Reinhart, P., Rongen, F., & Müller-Gärtner, H.-W. (2002) · IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) · doi:10.1109/nssmic.1995.510435 · Cited by 12
Inverse problems
Coleman, R. (1989) · Journal of Microscopy · doi:10.1111/j.1365-2818.1989.tb01475.x · Cited by 12
String-averaging expectation-maximization for maximum likelihood estimation in emission tomography
Helou, E. S., Censor, Y., Chen, T., Chern, I., Pierro, Á. R. D., Jiang, M. F., & Lu, H. H. (2014) · Inverse Problems · doi:10.1088/0266-5611/30/5/055003 · Cited by 11
A Novel Iterative MLEM Image Reconstruction Algorithm Based on Beltrami Filter: Application to ECT Images
Boudjelal, A., Elmoataz, A., Attallah, B., & Messali, Z. (2021) · Tomography · doi:10.3390/tomography7030026 · Cited by 11
Reconstruction algorithm for 3D Compton scattering imaging with incomplete data
Rigaud, G., & Hahn, B. N. (2020) · Inverse Problems in Science and Engineering · doi:10.1080/17415977.2020.1815723 · Cited by 11
Iterative tomographic reconstruction with TV prior for low-dose CBCT dental imaging
Friot--Giroux, L., Peyrin, F., & Maxim, V. (2022) · Physics in Medicine and Biology · doi:10.1088/1361-6560/ac950c · Cited by 11
Additive and multiplicative versions of the maximum a posteriori algorithm with median root prior
Mustafovic, S., & Thielemans, K. (2005) · IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) · doi:10.1109/nssmic.2001.1008688 · Cited by 11
Deconvolution of gamma-ray spectra obtained with NAI(Tl) detector in a water tank
Rahman, M. S., Cho, G., & Kang, B.-S. (2009) · Radiation Protection Dosimetry · doi:10.1093/rpd/ncp102 · Cited by 11
A Bayesian reconstruction method for micro‐rotation imaging in light microscopy
Laksameethanasan, D., Brandt, S. S., Engelhardt, P., Renaud, O., & Shorte, S. L. (2007) · Microscopy Research and Technique · doi:10.1002/jemt.20550 · Cited by 11
HST image restoration developments at the ST‐ECF
Adorf, H. M., Hook, R. N., & Lucy, L. B. (1995) · International Journal of Imaging Systems and Technology · doi:10.1002/ima.1850060407 · Cited by 11
Positron Emission Tomography and Random Coefficients Regression
Feuerverger, A., & Vardi, Y. (2000) · Annals of the Institute of Statistical Mathematics · doi:10.1023/a:1004141117010 · Cited by 11
Self-citation
Iterative continuous maximum‐likelihood reconstruction method
Mülthei, H. N. (1992) · Mathematical Methods in the Applied Sciences · doi:10.1002/mma.1670150405 · Cited by 11
Recovering convex edges of an image from noisy tomographic data
Goldenshluger, A., & Spokoiny, V. G. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871053 · Cited by 11
Shape-constrained uncertainty quantification in unfolding steeply falling elementary particle spectra
Kuusela, M., & Stark, P. B. (2017) · The Annals of Applied Statistics · doi:10.1214/17-aoas1053 · Cited by 11
Nonlocal total variation based dynamic PET image reconstruction with low-rank constraints
Zhang, Z., & Liu, H. (2019) · Physica Scripta · doi:10.1088/1402-4896/ab0854 · Cited by 11
Estimating the Weight Undersize Distribution for the Wicksell problem
Hoogendoorn, A. W. (1992) · Statistica Neerlandica · doi:10.1111/j.1467-9574.1992.tb01345.x · Cited by 11
Statistical models for PET and SPECT data
Kay, J. (1994) · Statistical Methods in Medical Research · doi:10.1177/096228029400300102 · Cited by 11
Iterative methods for the reconstruction of astronomical images with high dynamic range
Anconelli, B., Bertero, M., Boccacci, P., Carbillet, M., & Lantéri, H. (2006) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2005.06.049 · Cited by 11
Multiplicative Algorithms for Maximum Penalized Likelihood Inversion with Non Negative Constraints and Generalized Error Distributions
Ma, J. (2006) · Communication in Statistics- Theory and Methods · doi:10.1080/03610920500501478 · Cited by 11
A Solver for Dynamic PET Reconstructions based on Forward-Backward-Splitting
Benning, M., Heins, P., Burger, M., Simos, T. E., Psihoyios, G., & Tsitouras, C. (2010) · AIP conference proceedings · doi:10.1063/1.3498318 · Cited by 10
Fast inference of ill-posed problems within a convex space
Fernández-de-Cossio-Díaz, J., & Mulet, R. (2016) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2016/07/073207 · Cited by 10
Projection-to-image transform frame: a lightweight block reconstruction network for computed tomography
Ma, G., Zhao, X., Zhu, Y., & Zhang, H. (2021) · Physics in Medicine and Biology · doi:10.1088/1361-6560/ac4122 · Cited by 10
Iterative Algorithms in Inverse Problems
Byrne, C. L. (2006) · Cited by 10
Polytope samplers for inference in ill-posed inverse problems
Airoldi, E. M., & Haas, B. (2011) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 10
An Expectation Maximization Method for Joint Estimation of Emission Activity Distribution and Photon Attenuation Map in PET
Mihlin, A., & Levin, C. S. (2016) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2016.2602339 · Cited by 10
Superiorization of incremental optimization algorithms for statistical tomographic image reconstruction
Helou, E. S., Zibetti, M. V. W., & Miqueles, E. X. (2017) · Inverse Problems · doi:10.1088/1361-6420/33/4/044010 · Cited by 10
Maximum-Likelihood Expectation-Maximization Algorithm Versus Windowed Filtered Backprojection Algorithm: A Case Study
Zeng, G. L. (2018) · Journal of Nuclear Medicine Technology · doi:10.2967/jnmt.117.196311 · Cited by 10
Simultaneous estimation and segmentation from projection data in dynamic PET
Cui, J., Yu, H., Chen, S., Chen, Y., & Liu, H. (2018) · Medical Physics · doi:10.1002/mp.13364 · Cited by 10
High‐Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image Restoration
Zhang, J., Ma, M., Wu, Z., & Deng, C. (2019) · Mathematical Problems in Engineering · doi:10.1155/2019/2502731 · Cited by 10

Authors: Vardi, Y., Shepp, L. A., & Kaufman, L.
Affiliations: AT&T (United States) (US)
Venue: Journal of the American Statistical Association
Publisher: Informa UK Limited
Published: 1985-03
Volume: 80
Issue: 389
Pages: 8-20
ISSN: 0162-1459 (ISSN-L)
1537-274X
DOI: 10.1080/01621459.1985.10477119
OpenAlex: W1967374611
Cited by: 863
References: 27
Citations by year: 2026: 10 · 2025: 12 · 2024: 10 · 2023: 14 · 2022: 14 · 2021: 29 · 2020: 25 · 2019: 44 · 2018: 19 · 2017: 22 · 2016: 32 · 2015: 31 · 2014: 31 · 2013: 25 · 2012: 27
FWCI: 13.32
Type: journal article
Language: en
Open access: closed
Locations: Journal of the American Statistical Association (publishedVersion)
Topics: Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Medical Imaging Techniques and Applications
Physical Sciences › Mathematics › Mathematical Physics › Numerical methods in inverse problems
Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
Keywords: positron emission tomography, image reconstruction, statistical models, missing data, maximum likelihood estimation, expectation-maximization algorithm, method of moments, least squares, statistical estimation

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

A Statistical Model for Positron Emission Tomography

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks