IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. MI-1, NO. 2, OCTOBER 1982 teristics of a quad BGO detector for positron emission computed tomographs," in Proc. 3rd Symp. Physical and TechnicalAspects of Transmission and Emission Computed Tomography, Tokyo, Japan, Sept. 1980, pp. 94-95. [271 H. Murayama, E. Tanaka, N. Nohara, and T. Hayashi, ''Timing and positioning circuit for a quad BGO detector for a positron computed tomograph," in Proc. 3rd Symp. Physical and Tech- nical Aspects of Transmission and Emission Computed To- mography, Tokyo, Japan, Sept. 1980, pp. 96-97. (28] N. Nohara, E. Tanaka, H. Murayama, K. Ishimatsu, andT. Hayashi, "Performances of quad BGO detectors for positron emission computed tomography," in Proc. 4th Symp. Physical and Tech- nical Aspects of Transmission and Emission Computed To- mography, Tokyo, Japan, 1981, pp. 75-76. (29] H. Murayama, N. Nohara, E. Tanaka, and T. Hayashi, "A quad BGO detector and its timing and positioning discriminator for positron computed tomography," Nucl. Instrum. Meth., vol. 192, pp. 501-5 11, 1982. [30] T. F. Budinger, S. E. Derenzo, G. T. Gullberg, W. L. Greenberg, and R. H. Huesman, "Emission computer assisted tomography with single-photon and positron annihilation photon emitters," J. Comput. Assist. Tomogr., vol. 1, no. 1, pp. 13 1-145, 1977. [311 K. Takami, K. Ishimatsu, T. Hayashi, K. Ueda, F. Kawaguchi, K. Okajima, A. Ohgushi, S. Inoue, Y. Takakusa, S. Nakase, and E. Tanaka, "Design consideration for a continuously rotating positron computed tomograph," IEEE Trans. Nucl. Sci., vol. NS-29, to be published. Estimation of the Local Statistical Noise in Emission Computed Tomography N. M. ALPERT, D. A. CHESLER, J. A. CORREIA, R. H. ACKERMAN, J. Y. CHANG, S. FINKLESTEIN, S. M. DAVIS, G. L. BROWNELL, AND J. M. TAVERAS Abstract-A simple modification of the filtered backprojection algo- rithm is presented for the computation of the local statistical noise in emission computed tomography. The technique is general in that any distribution of radioactivity may be accommodated. When applied to positron emission tomography, it is shown that the effects of photon absorption, random coincidences, radioactive decay, and detector non- uniformity may be included. Calculations have shown the effects of resolution, object size, and photon absorption on the statistical noise of disk-shaped emitters. Comparison of calculation and experiment show close agreement both in magnitude and spatial variation. Measurements of the noise level in tomograms of the brain obtained during continuous inhalation of 150-C02 demonstrate that estimates of radioactivity concentration with a precision of a few percent are readily attainable. INTRODUCTION W rITHIN the limits imposed by finite spatial resolution, emission computed tomography provides an estimate of the radioactivity concentration at any point in the tomo- graphic plane. In order to take full advantage of the quantita- tive potential of emission computed tomography, it is essential to have reliable estimates of the precision of measurement. Without estimates of the precision, one cannot determine the significance of differences in radioactivity concentrations within a slice, compute the error propagated in the calculation of quantitative values, or compare results obtained with different techniques. By precision of measurement, we mean the varia- Manuscript received March 26, 1982; revised August 12, 1982. This work was supported by the National Institutes of Health, U.S. Public Health Services, under Research Grant NS 10828. The authors are with the Department of Radiology, Massachusetts General Hospital, Boston, MA 02114. tion in the computed value of local activity concentration due to the Poisson fluctuations in the projection data. Several investigators have studied the effects of statistical noise in emission computed tomography. Theoretical analyses have established the relationship among the rms noise, the number of detected events, and the spatial resolution for the case of a disk with uniform activity distribution [1], [2]. Somewhat more complicated geometries were systematically studied by Budinger et al. [3] using computer simulation, and algorithms for arbitrary activity distributions have been pre- viously derived [4]. The formulas and nomograms developed to date provide information useful in designing experiments, but cannot be directly applied to practical measurements. In the experimental situation, it is necessary to consider several additional contributions to the statistical noise. These include the effect of photon attenuation, corrections for varia- tion in detector uniformity and/or linearity, corrections for random coincidences in positron emission tomography (PET), corrections for scattered radiation, and the changes in statisti- cal quality due to radioactive decay during measurements with short-lived radionucides. In PET, the measured coincidence rate (prompt coincidences) can be considered to be the sum of the true coincidence rate, the random coincidence rate (time uncorrelated), and the prompt scatter rate. Prompt scatter is not easily measured, and is usually minimized by appropriate shielding of the tomograph, whereas random coincidence rates can be routinely estimated during each experiment. Neglecting the prompt scatter contribution, the true coincidence rate, which is directly and linearly proportional to the underlying quantity of radio- 0278-0062/82/1000-0142$00.75 © 1982 IEEE 142