Abstract
Detecting cancerous lesion is an important task in positron emission tomography (PET). Bayesian methods based on the maximum a posteriori principle (also called penalized maximum likelihood methods) have been developed to deal with the low signal to noise ratio in the emission data. Similar to the filter cut-off frequency in the filtered backprojection method, the prior parameters in Bayesian reconstruction control the resolution and noise trade-off and hence affect detectability of lesions in reconstructed images. Bayesian reconstructions are difficult to analyze because the resolution and noise properties are nonlinear and object-dependent. Most research has been based on Monte Carlo simulations, which are very time consuming. Building on the recent progress on the theoretical analysis of image properties of statistical reconstructions and the development of numerical observers, here we develop a theoretical approach for fast computation of lesion detectability in Bayesian reconstruction. The results can be used to choose the optimum hyperparameter for the maximum lesion detectability. New in this work is the use of theoretical expressions that explicitly model the statistical variation of the lesion and background without assuming that the object variation is (locally) stationary. The theoretical results are validated using Monte Carlo simulations. The comparisons show good agreement between the theoretical predications and the Monte Carlo results.
This work is supported in part by the National Institute of Biomedical Imaging and Bioengineering under grants R01 EB00363, R01 EB00194, and by the Director, Office of Science, Office of Biological and Environmental Research, Medical Sciences Division, of the U.S. Department of Energy under contract no. DE-AC03-76SF00098.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Fessler, J.A.: Penalized weighted least squares image reconstruction for PET. IEEE Trans. Med. Im. 13, 290–300 (1994)
Mumcuoglu, E., Leahy, R., Cherry, S., Zhou, Z.: Fast gradient-based methods for Bayesian reconstruction of transmission and emission PET images. IEEE Trans. Med. Im. 13, 687–701 (1994)
Fessler, J.A., Hero, A.O.: Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms. IEEE Trans. Im. Proc. 4, 1417–1429 (1995)
Bouman, C., Sauer, K.: A unified approach to statistical tomography using coordinate descent optimization. IEEE Trans. Im. Proc. 5, 480–492 (1996)
Barrett, H.H., Yao, J., Rolland, J., Myers, K.: Model observers for assessment of image quality. Proc. Natl. Acad. Sci. 90, 9758–9765 (1993)
Barrett, H.H., Wilson, D.W., Tsui, B.M.W.: Noise properties of the EM algorithm: I. theory. Phy. Med. Bio. 39, 833–846 (1994)
Wang, W., Gindi, G.: Noise analysis of MAP-EM algorithms for emission tomography. Phy. Med. Bio. 42, 2215–2232 (1997)
Soares, E.J., Byrne, C., Glick, S.: Noise characterization of block-iterative reconstruction algorithms: 1. theory. IEEE Trans. Med. Im. 19, 261–270 (2000)
Abbey, C.K., Barrett, H.H.: Observer signal-to-noise ratios for the ML-EM algorithm. In: Proceedings of SPIE, vol. 2712, pp. 47–58 (1996)
Hudson, H.M., Larkin, R.S.: Accelerated image reconstruction using ordered subsets of projection data. IEEE Trans. Med. Im. 13, 601–609 (1994)
Fessler, J.: Mean and variance of implicitely defined biased estimators (such as penalized maximum likelihood): Applications to tomography. IEEE Trans. Im. Proc. 5, 493–506 (1996)
Fessler, J.A., Rogers, W.L.: Spatial resolution properties of penalized-likelihood image reconstruction: Spatial-invariant tomographs. IEEE Trans. Im. Proc. 9, 1346–1358 (1996)
Qi, J., Leahy, R.M.: A theoretical study of the contrast recovery and variance of MAP reconstructions from PET data. IEEE Trans. Med. Im. 18, 293–305 (1999)
Qi, J., Leahy, R.M.: Resolution and noise properties of MAP reconstruction for fully 3D PET. IEEE Trans. Med. Im. 19, 493–506 (2000)
Stayman, J.W., Fessler, J.A.: Regularization for uniform spatial resolution properties in penalized-likelihood image reconstruction. IEEE Trans. Med. Im. 19, 601–615 (2000)
Bonetto, P., Qi, J., Leahy, R.M.: Covariance approximation for fast and accurate computation of channelized Hotelling observer statistics. IEEE Trans. Nucl. Sci. 47, 1567–1572 (2000)
Qi, J., Huesman, R.H.: Theoretical study of lesion detectability of MAP reconstruction using computer observers. IEEE Trans. Med. Im. 20, 815–822 (2001)
Fessler, J.A., Yendiki, A.: Channelized Hotelling observer performance for penalized-likelihood image reconstruction. In: Proc. IEEE NSS-MIC (2002) (to appear)
Xing, Y., Gindi, G.: Raid calculation of detectability in Bayesian SPECT. In: Proceedings of IEEE International Symposimum on Biomedical Imaging (2002) CDROM
Yavuz, M., Fessler, J.A.: Statistical image reconstruction methods for randomsprecorrected PET scans. Medical Image Analysis 2, 369–378 (1998)
Blake, A., Zisserman, A.: Visual Reconstruction. The MIT Press, Cambridge (1987)
Lee, S.J., Rangarajan, A., Gindi, G.: Bayesian image reconstruction in SPECT using higher oreder mechanical models as priors. IEEE Trans. Med. Im. 14, 669–680 (1995)
Barrett, H.H., Gooley, T., Girodias, K., Rolland, J., White, T., Yao, J.: Linear discriminants and image quality. Image and Vision Computing 10, 451–460 (1992)
Myers, K.J., Barrett, H.H., Borgstrom, M.C., Patton, D.D., Seeley, G.W.: Effect of noise correlation on detectability of disk signals in medical imaging. Journal of the Optical Society of America A 2, 1752–1759 (1985)
Myers, K.J., Barrett, H.H.: Addition of a channel mechanism to the ideal-observer model. Journal of the Optical Society of America A 4, 2447–2457 (1987)
de Vries, D., King, M., Soares, E., Tsui, B., Metz, C.: Effects of scatter subtraction on detection and quantitation in hepatic SPECT. J. Nucl. Med. 40, 1011–1023 (1999)
Yao, J., Barrett, H.H.: Predicting human performance by a channelized Hotelling model. In: Proc. of SPIE, vol. 1768, pp. 161–168 (1992)
Abbey, C.K., Barrett, H.H.: Observer signal-to-noise ratios for the ML-EM algorithm. In: Proc. of SPIE, vol. 2712, pp. 47–58 (1996)
Narayan, T., Herman, G.: Prediction of human observer performance by numerical observers: an experimental study. Journal of Optical Society of America A 16, 679–693 (1999)
Gifford, H., King, M., de Vries, D., Soares, E.: Channelized hotelling and human observer correlation for lesion detection in hepatic SPECT imaging. J. Nucl. Med. 41, 514–521 (2000)
Burgess, A.E., Colborne, E.: Visual signal detection. IV. obserer inconsistency. Journal of Optical Society of America A 5, 617–627 (1988)
Qi, J., Leahy, R.M., Cherry, S.R., Chatziioannou, A., Farquhar, T.H.: High resolution 3D Bayesian image reconstruction using the microPET small animal scanner. Phy. Med. Bio. 43, 1001–1013 (1998)
King, M., de Vries, D., Soares, E.: Comparison of the channelised hotelling and human observers for lesion detection in hepatic SPECT imaging. In: Proc. of SPIE, vol. 3036, pp. 14–20 (1997)
Abbey, C.K., Eckstein, M.P.: Optimal shifted estimates of human-observer templates in two-alternative forced-choice experiments. IEEE Trans. Med. Im. 21, 429–440 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Qi, J. (2003). Theoretical Evaluation of the Detectability of Random Lesions in Bayesian Emission Reconstruction. In: Taylor, C., Noble, J.A. (eds) Information Processing in Medical Imaging. IPMI 2003. Lecture Notes in Computer Science, vol 2732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45087-0_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-45087-0_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40560-3
Online ISBN: 978-3-540-45087-0
eBook Packages: Springer Book Archive