NON-UNIFORM ATTENUATION CORRECTION USING SIMULTANEOUS TRANSMISSION AND EMISSION CONVERGING TOMOGRAPHY

Transcription

1 1134 IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 39, NO. 4,1992 NON-UNIFORM ATTENUATION CORRECTION USING SIMULTANEOUS TRANSMISSION AND EMISSION CONVERGING TOMOGRAPHY C-H Tung, G. T. Gullberg, G. L. Zeng, P. E. Christian, E L. Datz, and H. T. Morgan University of Utah, Salt Lake City, Utah and Ohio Imaging of Picker International, Bedford Heights, Ohio Abstract Photon attenuation in cardiac single photon emission computed tomography (SPECT) is a major factor contributing to the quantitative inaccuracy and the decrease in specificity of lesion detection. A measured map of the attenuation distribution is used in combination with iterative reconstruction algorithms to accurately compensate for the variable attenuation in the chest. The transmission and emission data are acquired simultaneously using a multi-detector, fan-beam collimated SPECT system with a transmission line source (Tc-99m) precisely aligned at the focal line opposite one of the detectors and of a different energy than the emission source (Tl-201). The contamination of transmission data by the high energy photopeaks of T1-201 is removed based upon measurements from emission-only acquisition detectors. An algorithm was derived to eliminate scatter of Tc-99m transmission photons (140 kev) into the lower energy T1-201 window (73 kev) of all three detectors. The quantitative accuracy of cardiac SPECT is significantly improved using simultaneously acquired transmission and emission data which are obtained in a clinically acceptable patient scanning time. between TCT and SPECT images due to patient movement. With single detector SPECT systems, efforts have been made to reduce the scanning time by simultaneously acquiring transmission and emission data [7,8]. These attempts have used a flood transmission source mounted opposite a parallel-beam collimated detector. The disadvantage has been the contamination of transmission and/or emission data from crosstalk of transmission and emission sources. Additional disadvantages of parallel collimation are the large bulk and weight of the plane source and the poor counting statistics of the parallel beam geometry. Stronger transmission sources increase the statistics, but also increase the dose to the patient. The use of converging collimators such as cone-beam and fan-beam collimators requires placing the transmission source at the focus and has shown to increase transmission statistics. Arecent study [9] showed improved image quality using a cone-beam collimator and a transmission point source with activity as low as 3 mci. However, the disadvantage of converging 'collimation is the truncation of transmission data. A SPECT system with three detectors offers the ability to simultaneously acquire transmission and emission data in an acceptable clinical imaging time and reduces the crosstalk of 1. INTRODUCTION emission and transmission data. With fan-beam collimators good transmission statistics are obtained with a light weight In single photon emission computed tomography (SPECT), transmission line source containing a low dose of the quantitative measurement of isotope activity in specific organs and regions of interest is extremely difficult because of approximately 10 mci of radioactivity. The line source is positioned at the focal line opposite one of the detectors. the limited spatial resolution, large partial volume effect, and the effects of photon attenuation and scatter. Advancements in Transmission and emission data are simultaneously acquired in new Tc-99m radiopharmaceuticals, collimator design, and the this detector while the other two detectors simultaneously acquire emission data. In our work presented here, Tc-99m is development of multi-detector SPECT systems have used as the transmission source and T1-201 as the emission significantly improved resolution and sensitivity. In particular, the development of multi-detector SPECT systems now makes source. All three detectors acquire data from an acquisition window centered at 140 kev and another centered at 73 key it possible to simultaneously obtain emission and transmission Transmission and emission data from all three detectors are data and, for the first time, offers a reasonable approach to corrected for crosstalk before reconstruction. The transmission correcting for the variable attenuation in the thorax, a problem which has constantly plagued cardiac SPECT imaging. data are reconstructed to give the distribution of attenuation coefficients. The scatter-corrected emission proiections from all Two different approaches have been attempted to solve the three detectors are reconstructed io " produce the attenuation problem in SPECT. The first approach utilizes techniques which assume a uniform attenuator [ However, the variation of attenuation coefficients in the human chest can cause incorrect quantitative measurement of the uptake of radiopharmaceuticals in the heart if a uniform attenuator is assumed. The second approach utilizes transmission computed radiopharmaceutical distribution which is compensated for photon attenuation using the reconstructed attenuation coefficients. This paper presents the essential elements of the multidetector simultaneous acquisition and methods used to correct tomography (TCT) to determine the distribution of attenuation the data contaminated by energy crosstalk Of emission coefficients needed for the non-uniform attenuation correction and transmission to reconstruct the truncated transmission projection data, and to reconstruct the emission [5, 61. Usually a transmission study is performed prior to the emission study, but the separate acquisitions double the distribution corrected for attenuation. Results are given for both phantom and patient studies. scanning time and increase the chance of misregistration /92$03.00 Q 1992 IEEE

2 1135 Collimated Line source Line source holder Figure 1. Schematic diagram of the Picker Prism 3000 three-detector SPECT system with a transmission line source holder attached to detector #l. 2.1 Data Acquisition A. Imaging System 2. METHODS A PRISM 3000 SPECT system (Ohio Imaging of Picker Intemational, Bedford Heights, Ohio) was modified as shown in Figure 1 to perform the simultaneous transmission and emission data acquisition. A source holder was attached to the detector #1 using Velcro straps and elastic bands. The line source was secured to the source holder and was positioned so that it remained at the focal line as the detector traversed a body contouring orbit. The source was collimated so that an aperture of approximately 40" was obtained along the line source which was 50.8 cm in length and 1.2 mm in diameter. For the phantom and patient studies, the transmission source was Tc-99m and the emission source was T Low energy, high resolution fan-beam collimators were used. Two pulse-height energy windows were set. One 15% window was centered at 140 kev for the transmission data and one 30% window was centered at 73 kev for the emission data. Two sets of projections, one for each of the two energy windows, were acquired for each detector and were corrected for radionuclide decay. B. Phantom Study The phantom study was performed using a small circular Jaszczak cardiac phantom (Data Spectrum Corporation, Hillsborough, NC). The phantom consists of a cylindrical container with an inside diameter of 21.6 cm. A cardiac insert was placed inside the container. Two Styrofoam blocks were placed tightiy around the cardiac insert to simulate the lungs. The cardiac insert has two concentric chambers separated by 1.0 cm. Within the separation, two simulated lesions of solid acrylic blocks, one 4x4 cm and one 2x2 cm, were located to simulate cold defects in the myocardium. The space between the two chambers of the cardiac insert was filled with water containing a concentration of 1.12 pci/ml of T1-201 to simulate the myocardial uptake. The inner chamber of the cardiac insert and the rest of the cylinder were filled with a concentration of 0.05 pci/ml of T1-201 to simulate the background activity. For the phantom study, the line source was filled with 20 mci of Tc-99m. Both transmission and emission projection data were collected using a 50 cm focal length fan-beam collimator. The projections were digitized into 64x64 arrays. A total of 120 projections for each detector were sampled over 360' for both transmission and emission data, Each view was acquired for 15 seconds. For transmission projections, the minimum transmitted count was approximately 100 counts per projection bin with approximately 2000 incident counts per bin per view. For emission projections, the average total counts per view was approximately 30,000 counts. After acquiring the projection data, a static image of the line source was collected for 15 seconds with an average incident flux of approximately 2000 counts per bin. C. Patient Study The patient was exercised on a treadmill for 10 minutes using the standard Bruce protocol. The patient was exercised to a maximum heart rate of 165 beats per minute. One minute prior

3 1136 Focal Line Figure 2. Truncated projections. The cross-hatched sections indicate portions of the subject extending outside the field of view of the fan-beam collimator. Transmission line source Figure 3. Truncated incident flux. If the focal length is too long, the incident flux can be truncated using body contour orbits. to the termination of exercise, the patient was injected intravenously with approximately 3.1 mci of T Then the patient was transferred to the SPECT system for the standard parallel-hole cardiac SPECT study. The simultaneous transmission and emission study started approximately 3 hours after cessation of exercise. For the patient study, the line source was filled with 10 mci of Tc-99m. Transmission and emission data were collected using 65 cm focal length fan-beam collimators. The projections were digitized into 64x64 arrays. A total of 80 projections were sampled over 240" for each detector. Each view was acquired for 15 seconds. For transmission projections, the minimum transmitted counts was approximately 5 counts per projection bin. For emission projections, the average total counts per view was approximately 35,000 counts. A static flood image was collected after simultaneous acquisition for 15 seconds with an average incident flux of approximately 1000 counts per bin. 2.2 Data Processing A. Transmission Data (i) Crosstalk Correction The energy spectrum of T1-201 has 94.4% kev photons, 2.7% 135 kev gamma rays, and 10% 167 kev gamma rays per disintegration. A significant number of 135 and 167 kev T1-201 photons were detected in the transmission data acquired from the 140 kev energy window of detector #l. If no corrections were made, the distribution of attenuation coefficients would show a decrease in the attenuation coefflcients in the region of the heart. An estimate of the 135 and 167 kev photons of Tl-201 detected in the transmission data for the detector acquiring simultaneous transmission and emission data (detector #1) was obtained from the data acquired in the Tc-99m transmission energy windows (140 kev) of the two detectors acquiring emission data only (detectors #2 and #3). For 360" data acquisition, an estimate was obtained by taking the average of the 140 kev data of detectors #2 and #3 at the same view. If data were acquired over an angular range of less than 360", one instead of two samples may be all that can be obtained for some projection views. The estimated T1-201 photon contamination was subtracted from the transmission data of detector #1 before reconstructing the distribution of attenuation coefficients. (ii) Truncation Correction The magnification of the fan-beam geometry gave transmission projections which were truncated (Figure 2). Making the focal length longer would reduce the truncation but increases the potential of truncating the incident transmission flux (see Figure 3) when the detectors move in close to the body during body-contouring orbit acquisitions. We investigated both 50 and 65 cm focal length collimators and found that 65 cm was a better choice to minimize the truncation shown in Figure 2 without truncating the incident flux as illustrated in Figure 3. The transmission reconstruction problem was formulated such that the distribution of the attenuation coefficients was determined from the system of linear equations for only measured projections. An iterative EM reconstruction algorithm was used to solve this underdetermined system of linear equations by maximizing the likelihood function. The algorithm was constrained to reconstruct the attenuation distribution on a finite elliptical support. An estimate of the elliptical support was obtained from detector radius information provided by the system acquisition software. Since the camera followed close to the body during the noncircular orbit acquisition, the detector radius information could be used to approximate an elliptical body contour. An estimate of the elliptical support was obtained from left lateral, right lateral, and posterior radius information of the noncircular orbit and a physical anterior measurement of the separation between the patient and the detector. If necessary, this support could be further refined by observations of transmission reconstructions. (iii) Reconstruction The transmission data were converted to projections of linear attenuation coefficients by taking the natural logarithm of the ratio of the incident flux to the measured transmitted counts.

4 1137 Figure 4. Backscatter at position A. Illustration of the contamination of emission projection data due to downscatter of Tc-99m photons into the T1-201 energy window when the transmission source is at position A. Figure 5. Backscatter at position B. Illustration of the contamination of emission projection data due to downscatter of Tc-99m photons into the T1-201 energy window when the transmission source is at position B. STEP 1: P;+P; STEP 2: STEP3: I p; -p! I P;+Py-lP;-P;l b - Transmission line source These projections were then reconstructed using 8 iterations of the iterative EM algorithm [lo]. The initial solution for the reconstruction was set to zero outside and one inside the elliptical support. Because the EM algorithm is multiplicative, the zero values constrained the reconstruction to the elliptical support. Since the reconstructed attenuation coefficients were energy dependent, it was necessary to transform the reconstructed attenuation coefficients for the 140 kev energy of Tc-99m to the coefficients for the 73 kev energy of T The conversion was based on the assumption that the coefficient varies linearly between 140 kev and 73 key The estimated attenuation coefficient p, for T1-201 in tissue is [6]: H O H O where pt: = 0.184/cm, pt: = 0.153/cm, and ptc is the reconstructed linear attenuation coefficient for Tc-99m in tissue. For the emission reconstruction, attenuation factors were formed as exponentials of the partial line integrals of the attenuation distribution from the pixel of interest to the detector [ll]. These factors were calculated for every projection ray passing through the pixels inside the elliptical support. These factors were calculated only once and stored in the memory in order to speed up the EM algorithm.

5 I I 1138 Figure 8. Transaxial transmission CT images of the circular heart-lung phantom (A) and transaxial emission CT images of the cardiac phantom without attenuation correction (B) and with attenuation correction (C). Note the 4 cm (left) and 2 cm (right) defects. B. Emission Data (i) Crosstalk Correction The emission data were contaminated with transmission photons that downscattered in photon energy. As shown in Figures 4 and 5, transmission photons could backscatter from the patient and be detected in the 73 kev T1-201 energy window of the detectors (detectors #2 and #3) adjacent to the line source. Also, some fonvardscattered transmission photons (Figure 7) could be detected in the 73 kev energy window of detector #l. The T1-201 emission data were corrected for these two types of contamination of transmission photons so that emission data from all three detectors could be used. The intensity of the detected backscatter was found to decrease rapidly in the direction away from the line source as illustrated in Figure 6. When the line source was positioned at A (Figure 4) and B (Figure 5), the emission data sampled from detector #2 for position A and detector #3 for position B were equal. However, the detected transmission backscatter decreased in intensity from opposite ends of the data array. It was observed that in most of the projection data the profile of the backscattered photons decreased rapidly in the direction away from the line source so that the scatter profile in the data array at position A did not overlap with the profile in the data array at position B. Using this fact, a simple technique was developed to remove the detected backscattered transmission photons. Each step of the correction procedure is illustrated in Figure 6. First, the emission projection measurements from the two detectors were added together. Then, the emission data from one of the detectors (for example detector #3 at position B) was subtracted from the emission data from the other detector. The corrected emission data was obtained by taking the difference between the summed image and the absolute value of the difference image. For scans of less than 360", some projections did not have complimentary views. For those views the backscatter profile was estimated from other projections with similar anatomical projections to those that were not measured. This procedure corrected for the backscatter detected in the detectors adjacent to the line source. The fonvardscatter detected in the 73 kev energy window of the detector (detector #1) opposite the line source was eliminated based upon a method developed by Frey and Tsui [8]. A fraction ft of the crosstalk corrected transmission photons T, in each projection bin (the 140 kev window) was subtracted from the projection data E,,, for the same bin measured from the 73 kev emission window: E, = E, - ft x T,. (2)

6 1139 Figure 9. Short axis emission CT images of the cardiac phantom without attenuation correction (A) and with attenuation correction (B). Note the 4 cm (left) and 2 cm (right) defects. The fraction ft was determined by the water-equivalent thickness x of the absorber along the particular projection ray for that projection bin. If 70 is the incident flux, T is the transmission counts recorded after correcting for downscatter H20 from high energy T1-201 photons, and P,, is the water attenuation coefficient for photons at 140 kev, the expression for the factor is given by ft = ~10-~x ~10-~x~ ~10-~x~, (3) where The expression in equation (3) was determined from a least squares fit of ratios of data measured in the 140 kev window to data measured in the 73 kev window for various thickness of water equivalent absorber (30 cm x 22 cm) placed between a Tc- 99m line source and the detector. (ii) Reconstruction The corrected emission projection data were reconstructed using 20 iterations of the iterative EM algorithm. Fof each iteration an attenuated projection and backprojection operation [ 11,121 was performed. The attenuation factors were retrieved from on-board memory during the projection and backprojection operations. These factors were precalculated and stored in memory using the anatomically corresponding transaxial reconstructed attenuation distribution. The reconstructed emission transaxial images were filtered with a three-dimensional low-pass filter to reduce image noise. Then the transaxial images were reformatted to produce short axis, vertical long axis, and horizontal long axis displays. Figure 10. Profiles of a short axis slice through the cardiac insert without attenuation correction (left) and with attenuation correction (right). 3.1 Phantom Study 3. RESULTS Transmission and emission reconstruction results for the phantom study are shown in Figure 8. Transaxial slices of the distribution of attenuation coefficients are shown in Figure 8A. The simulated lungs (Styrofoam) can be easily delineated from the myocardium and surrounding water. Figure 8B shows the reconstructed emission transaxial slices obtained without attenuation correction. Septal regions are seen with markedly reduced uptake of radionuclide concentration. Figure 8C shows results after attenuation correction. Improved uniformity throughout the myocardium can be appreciated.

7 1140 Figure 11. Transaxial transmission CT images of cardiac patient study. Note the elliptical support surrounding the body. Short axis slices, with and without attenuation correction, are shown in Figure 9. Cold defects are seen in the emission images. Profile plots of a representative short axis slice are shown in Figure 10. Without attenuation correction, the profiles illustrate a lower uptake in the septum than in the lateral wall of the myocardium. With attenuation correction the lateral and septal wall are shown to have approximately equal concentration. The overall intensity increases approximately by a factor of four. 3.2 Patient Study The results of the cardiac patient study are shown in Figures 11 through 17. Transaxial reconstructions of transmission data are shown in Figure 11. Short axis slices are shown in Figure 12 and a profile for a representative slice is shown in Figure 13. Horizontal long axis slices are shown in Figure 14 and a representative profile in Figure 15. The profiles for the short axis and horizontal long axis slices show that equal count densities are obtained in the septal and lateral wall of the myocardium with attenuation correction. Vertical long axis slices are displayed in Figure 16 and a selected profile is shown in Figure 17. With attenuation correction the posterior portion of the inferior wall and anterior portion of the superior wall have nearly the same intensity. DISCUSSION The results of the phantom and patient experiments show that simultaneous transmission and emission computed tomography using a SPECT system with three detectors improves the quantitation of the uptake of T1-201 in the heart. The technical problems of truncated transmission projections and crosstalk between transmission and emission data were addressed. It was found that the use of 65 cm focal length fanbeam collimators with a line source positioned at the focal line minimized the truncation of the transmission projections of the chest without the detectors adjacent to the line source bruncating the incident transmission flux. The reconstruction of the truncated transmission projections using an iterative EM algorithm with an elliptical body contour support gave reasonable attenuation maps. Also, it was found that the geometrical positioning of the three detectors resulted in down scatter of transmission photons (140 kev) being detected in the lower emission energy windows centered at 73 kev of all three detectors. The application of a simple scatter correction technique to the emission data effectively subtracted out the contamination due to the downscatter. The attenuation corrected images of the heart show improved quantitation in the septum and posterior portion of the inferior wall of the left

8 14 1 Figure 12. Short axis emission CT images of the cardiac patient study without attenuation correction (A) and with attenuation correction (B). ventricle and qualitatively seem to indicate that the attenuation factors calculated from the estimated attenuation distributions are fairly accurate. A simultaneous acquisition has several advantages. It provides an attenuation map which is useful to correct for nonuniform attenuation and concurrently useful to provide the aligned anatomical information (the attenuation distribution) which helps the radiologist interpret the SPECT images. The simultaneous acquisition eliminates image misregistration that can occur from two separate scans. Also, the data are obtained in a clinically acceptable scanning time. In the selection of transmission sources, it is desirable to choose a source with a different photopeak energy than that of the emission source, preferably so that one radiation source has all its photopeak energies lower than those of the other source. In this case, at least one source will not be contaminated by downscatter from the other source. The combination of Tc-99m (emission source) and Gd-153 (transmission source) has been proposed [7]. This combination avoids the contamination of emission data and would be a good choice for the new Tc-99m myocardial agents. However, the availability and cost of Gd- I53 may make it prohibitive to use. If instead, Tc-99m is used for both emission and transmission sources, the transmission data are obtained from the detector obtaining the simultaneous transmission and emission data by subtracting estimates of the emission data obtained from the other two detectors. For this combination, emission data are lost from one of the detectors. In this paper, T1-201 was used as the emission source and Tc- 99m as the transmission source. This combination has to contend with the contamination of both transmission and emission data. However, Tc-99m is an appealing transmission source because of its availability, monoenergetic gamma ray emission (140 kev), and high photopeak efficiency. Important questions conceming detection sensitivity and specificity still need to be investigated. One consideration is whether the simultaneous acquisition degrades the emission data because of crosstalk between transmission and emission sources, so that detection sensitivity and specificity deteriorate Figure 13. Profiles of a short axis slice through the myocardium without attenuation correction (left) and with attenuation correction (right). even with attenuation correction. Another consideration is whether the attenuation factors are accurate enough for all patient sizes, especially considering the truncation problem with large patients, for the attenuation corrected images to be of improved diagnostic value. Also, the effects of increased reconstructed noise with attenuation correction has to be investigated. We have found through computer simulations that with the transmission and emission statistics used in our studies, the percent root-mean-squared (%RMS) error can increase from 13% for the uncorrected reconstructions to 15% for the

9 1142 Figure 14. Horizontal long axis emission CT images of the cardiac patient without attenuation correction (A) and with attenuation correction(b). attenuation corrected reconstructions [ 131. This difference is significantly improved with better emission statistics. The initial scanning configuration of all of our studies is illustrated in Figure 1. With future updates of gantry software, more flexibility in the selection of initial start and stop positions is expected. Previous experience with cardiac imaging would suggest that anteriorly scanning over 180" is preferred in order to increase the photon yield of the emission source especially for sources with low energy photons like TI-201. Using a scanning protocol of less than 360", it was necessary to modify the scatter correction method illustrated in Figure 6 for those projections which do not have complementary views. More phantom experiments and Monte Carlo simulations are needed to evaluate the present scatter correction technique and to develop new methods for less than 360" scans. Accuracy of the attenuation factors depends upon reconstructing truncated transmission projections using an iterative reconstruction algorithm. We have found through computer simulations and phantom experiments that even though the reconstructed transmission image is significantly distorted in the region outside the field of view, the attenuation factors (exponentials of the partial line integrals of the distribution of attenuation coefficients) which have the greatest influence upon the emission measurements are estimated fairly accurately. Supplying an approximate contour support for the transmission reconstruction improves the image quality of the transmission reconstruction and gives the best accuracy for the attenuation corrected emission reconstruction. However, the accuracy is only somewhat better than reconstruction without support. In summary, attenuation correction increases relative intensity in the posterior region of the inferior wall of the left ventricle and increases the relative intensity in the septum. Preliminary results of patient studies demonstrate attenuation correction may improve sensitivity and specificity. Figure 15. Profiles of a horizontal long axis slice without attenuation correction (left) and with attenuation correction (right). ACKNOWLEDGMENTS The research work presented in this manuscript was partially supported by NIH Grant R01 HL 39792, and Ohio Imaging of Picker Intemational. The authors thank Bill Nuttall for helping to build the transmission line source holder. We also thank Biodynamics Research Unit, Mayo Foundation for use of the Analyze software package.

10 1143 Figure 16. Vertical long axis emission CT images of the cardiac patient without attenuation correction (A) and with attenuation correction (B). REFERENCES J. A. Sorenson, Methods for Quantitative Measurement of Radioactivity in vivo by Whole-Body Counting, in Instrumentation in Nuclear Medicine, Vol. 2, ed. by G. J. Hine, J. A. Sorenson, Chap. 9,pp L. T. Chang, A method for attenuation correction in radionuclide computed tomography, IEEE Trans. Nucl. Sci., vol. 35, pp , April J. Tretiak and P. Delaney, The exponential radon transform, SIAM J. Appl. Math., vol. 39, no. 2, pp , G. T. Gullberg and T. F. Budinger, The use of filtering method to compensate for constant attenuation in single-photon emission computed tomography, IEEE Trans. Bio. Eng., vol. 28, no. 2, pp , Feb J. A. Malko, R. L. Van Heertum, G. T. Gullberg, and W. P. Kowalsky, SPECT liver imaging using an iterative attenuation correction algorithm and an extemal flood source, J. Nucl. Med., vol. 27, pp , B. M. W. Tsui, G. T. Gullberg, E. R. Edgerton, J. G. Ballard, J. R. Perry, W. H. McCartney, and J. Berg, Correction of nonuniform attenuation in cardiac SPECT imaging, /. Nucl. Med., vol. 30, pp , D. L. Bailey, B. F. Hutton, P. J. Walker, B. R. Zeeberg, and S. Loncari, Improved SPECT using simultaneous emission and transmission tomography, /. Nucl. Med., vol. 28, pp , E. C. Frey, B. M. W. Tsui, and J. R. Perry, Simultaneous acquisition of emission and transmission data for improved T1-201 cardiac SPECT imaging using a Tc-99m transmission source. J. Nucl. Med. (in press). S. H. Manglos, D. A. Bassano, C. E. Duxbury, and R. B. Capone, Attenuation map for SPECT determined using cone beam transmission computed tomography, IEEE Trans. Nucl. Sci., vol. 37, pp , K. Lange and R. Carson, Reconstruction algorithms for emission and transmission tomography, J. Comput. Assist. Tomogr., vol. 8, pp , G. T. Gullberg, R. H. Huesman, J. A. Malko, N. J. Pelc, and T. E Budinger, An attenuated projector-backprojector for iterative SPECT reconstruction, Phys. Med. Biol., vol. 30, no. 1, pp Figure 17. Profiles of a vertical long axis slice without attenuation correction (left) and with attenuation correction (right). U21 R. H. Huesman, G. T. Gullberg, W. L. Greenberg, and T. F. Budinger, RECLBL Library Users Manual-Donner Algorithms for Reconstruction Tomography, Lawrence Berkeley Lab., Berkeley, CA, Tech. Rep. PUB-214, U31 C-H Tung and G. T. Gullberg, Emission and transmission noise propagation in cardiac SPECT imaging with non-uniform attenuation correction, J. Nucl. Med. vol. 33, pp. 902, 1992.