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Clinical Investigations |
National Institutes of Health, Bethesda, Maryland
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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Key Words: PET • iterative reconstruction • image noise • lesion detection
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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FBP reconstructions have well-understood noise characteristics; in fact, one can easily compute the noise present in FBP images (6,7). Iterative algorithms such as OSEM (8,9), however, are nonlinear, and their noise properties are far more complex (10). Theoretic studies (11) and phantom studies (2) have shown that iterative reconstruction should achieve better noise characteristics than does FBP. In addition, when simulated lesions were inserted into brain images, improved lesion detection was reported with iterative, compared with FBP, reconstructions (12). However, because accurate measurement of noise from patient images is difficult, few, if any, quantitative analyses of OSEM-reconstructed image noise in real patient images have been performed (13). Justification for the clinical use of the OSEM algorithm for oncology rests, therefore, primarily on the perception that OSEM images "look" better than FBP images and on the above-mentioned theoretic and simulation studies. As promising as these may be, further quantitative analyses using actual patient data seem warranted. We report here the results obtained with an acquisition technique (7) that permits accurate measurement of noise in clinical images, independent of any noise in the transmission data (if used) or of true spatial variations in image intensity. We used this method to compare the noise in FBP-reconstructed clinical images with the noise in OSEM-reconstructed clinical images, both with and without attenuation correction (AC). Because image noise is an important component of tumor detection, these measurements provide further insight into how, and under what circumstances, iterative reconstruction might improve diagnoses in whole-body FDG PET oncology imaging.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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Data Acquisition and Processing
All datasets were acquired on an Advance PET scanner (General Electric Medical Systems, Milwaukee, WI) with 18 detector rings, yielding 35 slices at a 4.25-mm center-to-center slice separation (14). FDG whole-body studies were performed in 2-dimensional mode (septa in place). The acquisition time was 10–20 min per bed position, with 5 or 6 positions per patient. The scanner was coupled to a pulse generator with a 1-s period to generate 2 groups of 20 replicate measurements per slice (50 ms per gate), or 40 replicates in all. Each emission acquisition was immediately preceded or followed by an 8-min (ungated) transmission scan. The arms of the patients were outside the field of view. Transmission scans were low-pass filtered in the transverse plane (full width at half maximum [FWHM], 15 mm), the standard procedure in our institution, and corrected for emission contamination. Replicate acquisitions were obtained for 3 patients: 2 with colon cancer and 1 with breast cancer. Four representative slices, each containing 40 replicate sinograms, were selected from each patient for analysis. The total counts per replicate sinogram ranged from 7,000 to 10,000 before AC.
Each replicate was precorrected for random noise and was either preprocessed for AC or left attenuated. Scatter correction (14,15) was performed for AC datasets only. Random noise, scatter, and AC can induce negative values that are not compatible with the Poisson model used in OSEM. Negative projection values were clipped to zero before reconstruction. OSEM and FBP were applied to the same zero-clipped datasets to prevent potential bias. The sinogram bins were also grouped by pairs to a bin size of 4 mm instead of the originally acquired 2 mm. This step was found desirable because it increased the S/N in each of the short replicate images without introducing correlations in the projection data. Each replicate was reconstructed into a 128 x 128 image (pixel size, 4 mm) with FBP (ramp filtered) and OSEM (3 iterations, 21 subsets, roughly equivalent to 63 iterations of the regular expectation-maximization algorithm). We verified that the resolution obtained with this number of iterations matched the resolution obtained with FBP by analyzing anatomic features in the images (hot spots on AC and NAC images, skin on NAC images) and fitting profiles of those features to gaussian functions. Estimates of FWHM were equivalent for FBP and OSEM (average FWHM difference, 0 ± 1 mm) for 17 anatomic features with sizes ranging from 12 to 20 mm for both OSEM and FBP. All replicate images were subsequently filtered with a gaussian filter (FWHM, 8 mm) before computation of the mean and SD images of each set to increase the S/N of the short replicate images. SD images were further filtered (FWHM, 8 mm) to reduce the errors in SD estimates. S/N images were obtained by dividing the mean images by their respective SD images. Finally, we computed an image percentage improvement, in which the intensity of each pixel represented the percentage improvement resulting from use of one method (i.e., OSEM or FBP) rather than the other. Thus, we could compare the S/N for OSEM and FBP (either with or without AC) by:
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 | (Eq. 1) |
%IFBP vs. OSEM was, for each pixel, either the percentage improvement resulting from use of OSEM over FBP, if OSEM was better, or the percentage improvement resulting from use of FBP over OSEM, if FBP was better. An image was made of the percentage improvement to allow visual and quantitative assessment of where, and by how much, the S/N of one method exceeded that of the other.
Simulation
The noise measurements characterize the noise in a single replicate, not in the full acquisition (the sum of the 40 replicate gates). Mean and variance will scale linearly with the average total count level for FBP, because FBP involves linear processing. A simulation was performed to verify that S/N scaled appropriately with increasing total counts in the data when using OSEM, because OSEM is a nonlinear process. The reference image was of an anthropomorphic torso phantom. The distribution was segmented into 4 components: lungs, hot background, heart cavity, and heart wall. An activity level was assigned to each component (lungs = 3, hot background = 6, heart cavity = 2, heart wall = 10), and a sinogram was generated with the same acquisition parameters (e.g., matrix size and pixel size) as in the patient studies, leading to a total of 18,786 counts. From this sinogram, 40 replicate sinograms with Poisson noise were generated for 30 count levels ranging from 1,878.6 to 1,878,600 (average total number of counts per replicate sinogram). No effect other than Poisson statistics was simulated (i.e., attenuation, random noise, and scatter were ignored). All sinograms were reconstructed with OSEM (3 iterations, 21 subsets). The S/N was computed at each pixel. Those estimates were averaged over each component (e.g., lungs and heart wall), giving an estimate of the S/N for each component at each count level.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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Percentage difference images ([OSEM - FBP]/OSEM) showed only an approximately random scatter of pixels, indicating no large differences in intensity between OSEM and FBP. Drawing regions of interest (ROIs) (all but 3 of which are shown on the corresponding attenuation images at the bottom of Fig. 1) and computing the average percentage difference between OSEM-AC and FBP-AC showed OSEM-AC to be lower by 1% ± 3% in the liver area (5 ROIs on slice B, 7 on slice C), by 3% ± 2% in bright tumors (1 ROI on slice C, 2 on slice D—ROIs are not shown but were drawn around the tumors labeled with arrows in row 1), and by 6% ± 3% in the heart. OSEM-AC was higher by 10% ± 10% in the lung (8 ROIs), possibly because of the constraint requiring OSEM pixels to remain positive.
Non–attenuation-corrected FBP and OSEM images are shown in rows 3 (FBP-NAC) and 4 (OSEM-NAC) of Figure 1. The images show the typical behavior caused by not performing AC: falsely high intensity in the lung and signal loss toward the center of the body (causing severe inhomogeneity in the liver slices). Because of this signal loss, the hot spot in the periaortic region of slice A, which is clearly seen in the attenuation-corrected images (rows 1 and 2) with both FBP and OSEM, is no longer visible in either the FBP or the OSEM images with NAC (rows 3 and 4). There is also (erroneously) high apparent uptake at the surface of the body, where total attenuation is low. Just as in the comparison of FBP and OSEM with AC (rows 1 and 2 of Fig. 1), the OSEM-NAC images appear to have less noise than the FBP-NAC images, although the degree of improvement is visually less dramatic. Again, the intensity distributions and magnitudes of the OSEM-NAC and the FBP-NAC images (apart from noise) were quite similar. One should remember that for NAC images, intensity values (i.e., the "signal" in NAC images) do not reflect the true activity distribution. Indeed, because both algorithms attempt to reconstruct an image from inconsistent projections, difference images showed some noticeable patterns, in particular at very low intensity regions of the image, where artifacts caused by lack of AC were most apparent. Nonetheless, the overall observed intensity was similar for the two, as can be seen in rows 3 and 4 of Figure 1. ROIs indicated OSEM to be only slightly greater than FBP in the liver (5% ± 14%) and to be slightly less in the lung (4% ± 5%). For the tumors, FBP exceeded OSEM by only 5% ± 2%. For the heart ROIs, FBP was less than OSEM by 36% ± 42% (because of the large attenuation at the heart, intensity was near zero, so small differences caused large percentage differences).
To quantify the noise differences between FBP and OSEM, we used the replicate images to compute SD maps. The brightness of each pixel in the SD map was directly proportional to the SD of that pixel value, as computed from the replicate data. Figure 2 shows the SD maps corresponding to the mean images of Figure 1, displayed in the same order. The first 2 rows of Figure 2 allow comparison of the image noise (as measured by the SD) for FBP (row 1) and OSEM (row 2) when AC is applied. Each SD map in row 2 is displayed with its maximum-value pixel given maximum brightness, and the identical display range was used for the corresponding map in row 1. Therefore, every pair of SD images (e.g., the pair of SD maps for slice A, rows 1 and 2, and the pair of SD maps for slice B, rows 1 and 2) is displayed on the same brightness scale and so can be directly compared visually. The SDs of the FBP images (row 1, Fig. 2) appear fairly uniform, showing little of the structure in the corresponding mean images (row 1, Fig. 1). In contrast, the SD maps of the OSEM images (row 2, Fig. 2) look similar to the corresponding mean images of Figure 1, except for the slightly reduced contrast. The noise at a pixel in the OSEM images seems strongly related to the intensity value of the corresponding pixel in the mean image. The SD values are high where the original image intensity (from Fig. 1) was high, and the SD is low where the original image intensity was low.
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Figure 3 shows S/N images depicting the ratio of the signal intensity at each pixel to the noise at each pixel obtained by dividing the mean images of Figure 1 by the SD images of Figure 2. The S/N images of Figure 3 are all displayed on a single common gray scale (with S/N values > 2.2 set to maximum brightness) and are displayed in the same order as in Figures 1 and 2. Therefore, one can directly compare (visually) the S/N values between all the images of Figure 3. All S/N images had a similar range, despite the differences in AC and in the reconstruction algorithm. The S/N images for OSEM and FBP have a drastically different structure: FBP S/N images (rows 1 and 3 of Fig. 3) show a high S/N where the intensity is high and a low S/N where the intensity is low. OSEM S/N images (rows 2 and 4 of Fig. 3) are, on the other hand, much more uniform across the image.
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Row 2 of Figure 4 compares OSEM and FBP for the case when NAC is applied. In the lungs, only slight or near-zero improvement is seen using OSEM (dark red color). The more attenuated regions of the body (heart, mediastinum, and other soft tissue) had a much greater improvement with OSEM than with FBP. The exceptions are the tumors themselves, which again had a better S/N with FBP than with OSEM (dark blue colors). The same lung, liver, heart, and tumor regions as above were applied to the non–attenuation-corrected images, yielding an average percentage improvement for OSEM of 46% ± 13%, 84% ± 40%, 125% ± 49%, and -43% ± 7%, respectively.
Figure 5 shows the S/N plot with respect to the count level on a log–log scale for the simulated data. A regression over log(S/N) showed that the S/N was a linear function of the square root of the average count level (regression coefficient of 1.00 for all components of the simulated distribution). Therefore, the results of Figures 2–4 are expected to hold true even for count levels considerably above or below the 7,000–10,000 counts per replicate measured for the patients we studied.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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As mentioned previously, the linearity of the FBP process allows one to make theoretic predictions of the noise that will occur in a real, clinical FBP image. The nonlinearity of the OSEM algorithm makes such a computation exceedingly difficult (to our knowledge, it has never been achieved for clinical images) and is the reason that many previous investigations were based on simulations. Haynor and Woods (17) proposed an elegant "bootstrap/jackknife" method for creating a sort of "pseudo-replicate" dataset based on certain statistical assumptions, using list mode acquisitions. Using the gated replicate measurement method, we could make direct S/N measurements on actual clinical FDG PET scans without relying on any assumptions or simplifications that might be necessary in some simulations. These replicate measurements were then used to determine whether OSEM resulted in S/N improvement over the FBP method, and if so, in what parts of the image and by how much. Such a comparison is meaningful only if the resolution of the 2 reconstructions is matched. Resolution assessment is straightforward for FBP-reconstructed images but complex for OSEM images, because at the limited number of iterations used here and in clinical practice, resolution may differ for different objects within the image, depending on their relative size and intensity (18). By selecting several structures in the actual image data and inferring resolution from those structures, we believed we had objectively determined the number of iterations required, although the finite size of the objects used made such determinations difficult. Nonetheless, our choice of 63 effective iterations was slightly greater (and therefore more in favor of FBP in terms of noise) than that of Llacer et al. (11), who showed OSEM and FBP to match with a ramp filter after 35–45 iterations, and was similar to that of Meikle et al. (2), who optimized the number of iterations according to tumor size, with a minimum of 8 iterations and a maximum of 64 iterations. Certain unusual distributions of uptake for which the number of iterations used here may be insufficient are possible (19) and may introduce some bias. If more iterations are needed, the noise in the OSEM images will be higher. However, we believe that the situations studied here spanned a reasonably wide range of practically encountered clinical situations.
The data from Figure 1 showed that FBP and OSEM gave nearly identical signals, especially when AC was applied. That is, apart from noise differences, the mean intensity of the 2 image sets was very similar. Therefore, the S/N comparison reduces to a comparison of noise. Figure 2 shows the image noise for OSEM and FBP. FBP produces noise that is quite uniform throughout the image. The noise is almost completely uniform when NAC is applied but is still relatively uniform even with AC. This phenomenon had been predicted (6,20) from theoretic considerations. Most of the noise is caused by high-count projection lines. Even though high-count projection lines have a low percentage of noise, they have high absolute noise that, when backprojected across low-count areas (e.g., the lung), produces a high percentage of noise in the low-count regions. This is the reason that noise in the lung regions of FBP images is so high. The OSEM algorithm behaves differently. When a pixel value is high, the noise at that pixel is high, and when a pixel value is low, the noise is low. The noise from hot pixels does not spread out over other pixels, as with FBP. This is seen clearly in Figure 2, and this general behavior has been suggested by theoretic considerations (10,11). We expect OSEM, therefore, to most surpass FBP in regions of the image where counts are comparatively low. This is exactly what is observed in Figures 3 and 4: the lungs show the greatest improvement with OSEM in the attenuation-corrected images. In hotter areas, FBP and OSEM have a comparable S/N and there is less to be gained by using the OSEM method. In fact, in the very localized hot tumors examined in this study, FBP actually had a better S/N than did OSEM. These hot local tumors, however, already had such a high S/N that their detection might be less at issue. Interestingly, without AC, OSEM most surpasses FBP in the most attenuated areas, not in the lung. This finding is expected because, with NAC, the most attenuated areas have lower measured relative uptake.
The data of Figure 4 show that in most parts of the image, OSEM produces a better S/N than does FBP. This finding is true regardless of whether AC is performed. The improvement was greatest in the dimmer parts of images that contained both low-intensity and high-intensity regions and was smallest in the brighter parts of the images. In fact, FBP gave a better S/N at the site of the tumors themselves. Therefore, it is possible that OSEM would not improve detection of bright tumors embedded in a hot background (e.g., tumors in the liver). This possibility is consistent with our findings from the liver tumor of Figure 4 with AC. In those data, although S/N in the normal liver background tissue improved 21% with OSEM, S/N in the hot tumor was reduced 41%. The situation would be different for a less intense tumor, especially if it were in a lower intensity background region such as the lungs (with AC), where the improvements in S/N were found to be greater than 100%, and especially if the tumor had an intensity not much greater than background intensity. Such marginally detectable tumors would presumably be the most clinically interesting circumstance, and our data suggest that the S/N in such tumors would be significantly better with OSEM, making their detection easier with OSEM than with FBP. However, tumor detection depends on many other factors besides the S/N of the tumor—most notably on the relative signal and noise in both the tumor and its surrounding tissue.
The one situation not studied here was that of tumors near a hot bladder (as studied by Schiepers et al. (13)). The arguments above indicate that OSEM would produce a large percentage improvement over FBP in this situation (as supported by the data of Schiepers et al.).
One might think that the dataset used here to compare FBP and OSEM could be used equally well to quantitatively compare noise in attenuation-corrected and non–attenuation-corrected image sets. Unfortunately, comparisons of AC versus NAC are more difficult than comparisons of FBP versus OSEM. The "signal" itself is very different between AC and NAC images, as is the tumor-to-background contrast. In NAC images, the tumor-to-background contrast can also vary markedly from one side of the tumor to the other, because signal falls off so rapidly toward the center of the patient. The validity of using the S/N image for comparing AC and NAC images is made suspect by these difficulties, and for this reason, we did not attempt such comparisons.
Finally, the knowledge of each pixel’s variance does not describe the noise entirely. Noise texture was not considered, and it is possible that differences in noise texture exist between FBP and OSEM and that some observer retraining will be required to optimize visual interpretation of OSEM images.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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FOOTNOTES |
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For correspondence or reprints contact: Stephen L. Bacharach, PhD, Bldg. 10, Room 1C401, National Institutes of Health, Bethesda, MD 20892-1180.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONCONCLUSIONREFERENCES |
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