British Journal of Radiology (2004) 77, 323-328
© 2004 British Institute of Radiology
doi: 10.1259/bjr/78576048
The addition of computer simulated noise to investigate radiation dose and image quality in images with spatial correlation of statistical noise: an example application to X-ray CT of the brain
A J Britten, PhD
M Crotty, MSc
H Kiremidjian, MSc
A Grundy, FRCR
and
E J Adam, MRCP, FRCR
Departments of Medical Physics and Diagnostic Radiology, St George's Healthcare NHS Trust, London SW17 0QT, UK
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Abstract
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This study validates a method to add spatially correlated statistical noise to an image, applied to transaxial X-ray CT images of the head to simulate exposure reduction by up to 50%. 23 patients undergoing routine head CT had three additional slices acquired for validation purposes, two at the same clinical 420 mAs exposure and one at 300 mAs. Images at the level of the cerebrospinal fluid filled ventricles gave readings of noise from a single image, with subtraction of image pairs to obtain noise readings from non-uniform tissue regions. The spatial correlation of the noise was determined and added to the acquired 420 mAs image to simulate images at 340 mAs, 300 mAs, 260 mAs and 210 mAs. Two radiologists assessed the images, finding little difference between the 300 mAs simulated and acquired images. The presence of periventricular low density lesions (PVLD) was used as an example of the effect of simulated dose reduction on diagnostic accuracy, and visualization of the internal capsule was used as a measure of image quality. Diagnostic accuracy for the diagnosis of PVLD did not fall significantly even down to 210 mAs, though visualization of the internal capsule was poorer at lower exposure. Further work is needed to investigate means of measuring statistical noise without the need for uniform tissue areas, or image pairs. This technique has been shown to allow sufficiently accurate simulation of dose reduction and image quality degradation, even when the statistical noise is spatially correlated.
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Introduction
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There is concern to reduce radiation dose in X-ray procedures, and particularly CT scanning [1]. Reducing patient dose by reducing X-ray exposure has the inevitable consequence of increasing statistical noise in the images, and the key question is to identify the minimum X-ray exposure, i.e. poorest image quality, required for a given examination and pathology. The answer may be found by performing receiver operating characteristic (ROC) studies of patient groups under a range of different image qualities, where statistical noise is the relevant image quality parameter to be varied through mAs reduction.
X-ray CT studies have been performed with repeat scanning at reduced mAs [2–6], or with cadaver studies [7] to avoid the ethical issues of repeated scans. Such studies have had limited power to set minimum exposure factors due to the understandably limited numbers of patients studied. With dose reduction studies with low subject numbers the question usually remains of the reduction in sensitivity which would be achieved in the total patient population given the extremely limited number of equivocal or difficult cases studied.
The addition of noise to real CT studies by computer simulation has been implemented as a way of producing a range of scans with noise equivalent to reducing dose levels [8, 9]. This offers the prospect of being able to perform large-scale studies to evaluate diagnostic accuracy as a function of reducing dose by artificially increasing the image noise. The technique requires access to the raw projection data, and addition of the level of statistical noise appropriate to the lower exposure level prior to reconstruction.
The technique presented here provides a simulation of reduced exposure through the addition of statistical noise to pixel values in the final diagnostic image, applied for illustration to CT images after reconstruction. In principle, modification of the raw data is ideal since the assessment of statistical noise in the data is easier, and since the filtered back-projection reconstruction introduces a high degree of correlation into the final image noise [8]. There are, however, practical considerations that make it valuable to determine whether statistical noise can be added to images with significant spatial correlation of random statistical noise. The first consideration is that modification of raw data prior to reconstruction requires detailed data modification on the clinical CT scanner, and this is not currently an option, with work so far being carried out with specially provided software running on the clinical system [8, 9]. In contrast it is simple to export a reconstructed image and carry out the image modification on any computer with no risk to the clinical system. Second, every CT scanner site has access to a substantial archive of clinical cases. Images with difficult low-contrast pathology may be found from the existing archive, and these specific images may be degraded to statistical noise levels corresponding to low-dose studies. This retrospective analysis may also be carried out for the raw data manipulation technique, providing the raw data is archived, but we are aware that many sites do not archive raw data once the study has been reconstructed and reported.
The principles of computerized noise addition may be applied to other diagnostic imaging modalities, since spatial correlation of random statistical noise commonly occurs in imaging systems. This work aims to illustrate and validate the method of simulating exposure reduction through the addition of computer generated spatially correlated noise. The hypothesis is that computer simulated statistical noise can be added to a clinical image to simulate accurately how the same image would appear if taken at a reduced exposure.
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Methods
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We describe an example of the method applied to X-ray CT of the head, with evaluation of the effects of noise through observing the change to detection of periventricular low density white matter disease (PVLD). PVLD was chosen since it occurs relatively commonly in elderly subjects, is a low contrast change and therefore its identification may be affected by the image noise level. It is also adjacent to the lateral ventricles of the brain, whose uniform cerebrospinal fluid (CSF) liquid filling provides an opportunity to measure local statistical noise directly from the images. The skull at this level contains none of the features likely to produce streak artefacts, and hence images at this level should contain low levels of structured noise.
Starting with an image at a known exposure, statistical noise (the standard deviation of CT number within a region) in the image was measured and the expected increase in noise at a reduced exposure was calculated and added to the initial image. All scanning was carried out on a GE9800 CT scanner (IGE, Milwaukee, WI), and all images were reconstructed with the standard head algorithm. Images from 16 cm diameter water phantom were acquired with the same factors as used for patient images (120 kV, 140 mA and 3 s scan time). These images were used to calculate the autocorrelation function of noise in the reconstructed CT image. The expected relationship between image noise and exposure was checked by scanning the water phantom at a range of mAs values. These uniform images were also used to find how noise varied with radial distance from the centre of the phantom.
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Simulation and addition of correlated statistical noise
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The standard deviation of CT numbers from a region of interest (ROI), 
(E1), is the noise corresponding to the exposure setting E1 mAs. We wish to add statistical noise by altering the CT numbers to give a standard deviation (E2) corresponding to a lower exposure setting E2 mAs. The main noise source, within the clinical exposure range, is from X-ray detection, giving a ratio of the noise levels at the two exposures as (E2)/(E1)=
E1/E2 from which (E2) was calculated.
The noise distributions are independent, so the standard deviation of the noise distribution to be added, (add), was found from the following 2(E2)=2(E1)+2(add). Normally distributed noise with standard deviation CF x (add) and mean zero was generated and the values stored in a 512 by 512 image matrix to create a noise image. The multiplying factor CF is a factor required to account for the smoothing effect of correlation when applied by this method, as explained below. The noise autocorrelation function, ACF, was measured from the uniform water phantom image [10, 11]. The ACF was found to be zero at more than 2 pixels separation for the standard head reconstruction algorithm. The ACF factors were used as weights in a 5 by 5 convolution filter which was convolved with the noise image to produce the correct spatial correlation of the noise. The resulting correlated noise image was added to the original CT image to produce the simulated image. The need for the noise multiplying factor CF above is due to the method of image convolution to produce the correct spatial noise correlation, with CF representing the ratio of the standard deviations of the noise image before correlation to that after the correlation filter had been applied. The factor CF was found empirically. Several noise images were generated with Poisson distributed noise over a range of standard deviations, (N). These images were smoothed with the ACF kernel, and the resulting standard deviations (C) of the correlated distributions were read out. This gave a linear relationship between the required correlated noise magnitude, (add), and the magnitude of the Poisson distributed noise (P) which was used to generate the noise image. The regression line is (N)=3.06 (C), R2=0.99, so CF=3.06.
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Patients and scan protocol
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23 subjects were recruited, aged over 69 years, Caucasian to avoid effects of different skull vault thickness, and undergoing routine head scanning. Exclusion criteria were recent severe head trauma, intracranial mass lesions, major haemorrhages, or inability to co-operate. Following routine head scanning at an angle of 10–15° to the orbital meatal (OM) line, the plane of interest was identified at typically 4–6 cm above the base of the skull. On this slice we visualize the frontal and occipital horns of both lateral ventricles, the foramen of Monro, basal ganglia and internal capsule (Figure 1
). Two further images were acquired at this level at standard clinical exposures of 120 kV, 140 mA and 3 s scan time (420 mAs), and the tube current was immediately reduced to 100 mA and a slice acquired (300 mAs). The additional scans increased the radiation dose by approximately 15%. The local research ethics committee approved the protocol.
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Figure 1. CT transaxial slice showing typical positions of regions of interest (ROI) for the periventricular low density lesion (PVLD) areas and the ventricles.
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Patient image analysis and noise addition
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Standard deviations of pixel number from left and right ventricular ROIs were averaged to provide an estimate of noise in the ventricles. The ventricle noise measurement from a single image was compared with the noise measurements in subtracted image pairs, since agreement would support the assumptions that structured noise is low at this anatomical level, and would also confirm that the CSF is indeed a uniform density region. PVLD regions were drawn just superior to the right and left superior horns of the ventricle (Figure 1
). The noise in the PVLD ROIs was taken as an average of left and right PVLD ROIs, read from the image formed by subtraction between image pairs at 420 mAs. Subtraction was necessary to remove variations due to tissue structure. All noise readings from subtracted image pairs was divided by 2 to correct for the increased standard deviation from the subtraction. Comparing ventricular noise from a single image with the PVLD noise in subtracted image pairs tested the agreement between noise measurements in the ventricles and in the periventricular area.
The mean noise in the ventricles read from the 420 mAs exposure image was used to calculate the amount of statistical noise to add to simulate exposures at 340 mAs, 300 mAs, 260 mAs and 210 mAs, and the correlated noise was added to the initial 420 mAs image as described above. An estimate of the coefficient of variation (CV) in the reading of image noise from a ventricular ROI was obtained by performing 5 repeat measurements of pixel standard deviation on a 420 mAs image from each patient. The mean and standard deviation of these 5 readings per patient were calculated and the mean CV calculated from all 23 patients.
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Image evaluation
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The simulation of exposure was checked by comparing the measurements of ventricular noise in the 300 mAs acquired and simulated images. All images were printed onto film for viewing. Two experienced CT radiologists performed side-by-side comparison of both 300 mAs acquired and simulated images. The observers were asked to rank the degree of difference between the two films on the following scale:
1. Identical or only slight non-significant differences
2. Some differences, possibly significant
3. Noticeable, significant differences.
The observers viewed each image at 420 mAs and 300 mAs acquired, and 340 mAs, 260 mAs, 210 mAs simulated, and answered the following questions: Does the patient have PVLD? (Y/N). How would you rate the visibility of the internal capsule? (Good, average, poor). Images were presented one at a time on film, selected in random order from all the images in the whole study. The results on the diagnosis of PVLD for each observer were analysed separately for each observer, taking the observers own diagnosis from the 420 mAs image as the correct diagnosis for that patient, since this should provide the best quality image and no independent PVLD measurement is available. The accuracy of PVLD diagnosis relative to the diagnosis from the 420 mAs image was calculated at each exposure level.
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Results
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The expected relationship between image noise and mAs was confirmed by linear regression between and 1/mAs (R2=0.99, =60.58/mAs) from the water phantom data. Noise varied only slowly with increasing radial distance in the water phantom, dropping at the fractional rate of 0.016 cm–1. The ACF calculated from the uniform water phantom images showed insignificant correlation beyond two pixels, with ACF values of 0.74, 0.12 and 0 at pixel separations of 1, 2 and 3, respectively (with the ACF value 1 representing perfect correlation and 0 no correlation).
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Noise readings from clinical images
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The mean coefficient of variation of the ventricular noise reading from a single image was 5.4%, and this is used as an estimate of error in Figures 2–4. Ventricular noise measurements in single and subtracted 420 mAs images generally showed good agreement, with the mean difference of 11% and with only 4 of the 23 readings differing by more than 20% (Figure 2). Similarly there was generally good agreement between the ventricular noise from a single image and the PVLD region noise from a subtracted image pair, with a mean difference of 10% (non-significant) and only 2 of 23 readings differing by more than 20% (Figure 3).
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Figure 2. Statistical noise (standard deviation of CT number) from ventricular regions measured in a single image and from the result of subtraction between an image pair. The error bars represent a coefficient of variation of 5.4%.
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Figure 3. Statistical noise (standard deviation of CT number) from ventricular regions in single images versus noise in adjacent periventricular low density lesion (PVLD) regions measured from subtracted image pairs. The error bars represent a coefficient of variation of 5.4%. ROI, region of interest.
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Figure 4. Statistical noise (standard deviation of CT number) in ventricular regions measured from images acquired at 300 mAs, and simulated at 300 mAs based on original images at 420 mAs. The error bars represent a coefficient of variation of 5.4%.
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Comparison of ventricular noise in the simulated and acquired 300 mAs images shows a 14% mean difference (non-significant), with 6 of 23 values being more than 20% different (Figure 4).
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Subjective evaluations
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In comparing the 300 mAs acquired and simulated images there were grade 3 differences (noticeable significant differences) for observer B in 4 of the 23 image pairs, but none for observer A (Table 1). In the randomized individual image evaluation of the 300 mAs acquired and simulated images, diagnosis changed in one case for observer A, and in 4 of 23 for observer B. For all cases with changed diagnoses the pairs of images had been rated as identical or slight non-significant differences when viewed together. One set of patient films was lost and only 22 sets of data were available for subsequent scoring. There were no significant changes in diagnostic accuracy with reducing exposure (Table 2), though the high uncertainty (>±6%) in the accuracy percentages with these low patient numbers is noted. The visibility of the internal capsule becomes poorer as dose falls (Table 3).
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Table 1. Observer rating of differences between the 300 mAs acquired and the 300 mAs simulated image. The 300 mAs simulated image was based on original images at 420 mAs acquired image
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Table 2. Accuracy for the diagnosis of periventricular low density lesion for each radiologist, as exposure is varied. The gold standard diagnosis for each radiologist is their diagnosis on the 420 mAs acquired image
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Discussion
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This work has taken a special case, a CT slice at the level of the lateral ventricles, in order to allow validation of a general methodology of computerized noise addition, with the effects of spatial correlation included. The procedure requires an initial measurement of statistical noise in soft tissue regions, and uniform areas such as fluid filled spaces, can be used to estimate noise. Others have used liver tissue [2] or the blood filled thoracic aorta [8]. The noise addition in this study has assumed the same noise level over the whole of the image. Though variations in image noise were shown to be low in a uniform water phantom, larger variations are likely to occur either close to bony structures, or across asymmetric body parts such as the shoulders. Visual assessment of the subtracted images pairs was judged to show little variation in noise level, but this was not measured. Further development is required to produce methods of measuring local image noise when no uniform area is available, and the method would then be modified to add different amounts of noise across the image.
The importance of the spatial correlation of noise has been emphasised by previous work [8], and this importance will vary with amount of image correlation, influenced for example by the sharpness of the reconstruction filter used in CT. It has been shown to be simple to introduce the correct noise correlation to the added noise, based upon measurements that the user can simply perform with uniform test objects.
The accuracy of the noise addition process has been checked by the acquisition of a slice at 300 mAs and the simulation of the same image based upon the 420 mAs image. It was shown that the process can accurately achieve a target noise level. Subjective assessment of the images is important in addition to the objective measurements. Some significant differences were noted by one observer (4 out of 23 images), but none by the other. It is possible that some of these differences may be attributable to slight patient movement between the 300 mAs and 420 mAs acquired images, though no quantitative checks for movement were performed. There were changes in diagnosis of PVLD between the acquired and simulated 300 mAs images, representing a difference in 4% of cases and 17% of cases for observers A and B. This may represent the variability in repeat readings of this subtle lesion, but unfortunately no repeat readings of identical images were performed.
The diagnosis of PVLD was taken as an example to illustrate how the methodology could be used to assess the effect of exposure level on diagnostic accuracy, for a low-contrast lesion. ROC analysis would be ideal, and could be carried out reliably with a larger number of positive patients, but only between 6 and 11 patients were judged to be positive for PVLD (observers A and B, respectively). The diagnostic accuracy of the diagnosis did not change significantly as exposure was reduced by up to 50%, but this result must be treated with caution since the errors on the accuracy figures are large given the small number of patients. However, this illustrates the potential of the simulation method to reach an objectively judged minimum dose level. We note that the term diagnostic accuracy, in this PVLD example, may be more correctly termed "diagnostic constancy" or precision, since there is no gold standard identification of PVLD, and we have used the observers own diagnosis at the best image quality as the gold standard. This is not, however, a real difficulty with the technique, since it is highly meaningful to define the radiologists own diagnosis at the highest exposure level as the gold standard and ask at what reduced exposure level their decision changes, or becomes less certain. The visualization of the internal capsule, a low contrast structure, was selected as a good marker of image quality, but the criteria of the Commission of the European Community working group [12] could also be adopted in any future application.
Uncertainties in the original noise level, and therefore the amount of noise to add, result in errors in the final simulated noise level for the reduced mAs. This is equivalent to an uncertainty in the exposure level to which the slice corresponds. These results show that the noise levels can be measured and simulation achieved to a mean error of around 14%, with only a few images differing by more than 20%. Since the noise varies with the square root of the exposure, this 14% error in noise is equivalent to an uncertainty in dose of 30%. In considering clinical application of the results of such simulation studies it may be wise to increase the final exposure level by the fractional uncertainty in the measurement. This principle applies even to methods adding noise to raw data before reconstruction, where there will be an uncertainty in the estimated noise to be added.
There is no doubt that the ideal method to add noise is to access the data as early on in the imaging chain as possible, since each step in the chain may introduce spatial correlation. For CT this means modifying the projection data, as reported by Mayo [8]. This raw data modification requires a degree of access to commercial systems which is not widely available, and in other modalities such as image intensifier or digital detector flat panel imaging the "raw data" prior to filtering may not be available for modification. In this case the simple methodology described here will allow addition of realistic noise. The raw CT data is also only rarely archived in many centres, and so the only method available for application to the potentially rich archive of interesting equivocal and rare cases is a method that modifies the final image.
In conclusion, this work has shown that it is possible to simulate reduced radiation exposure in X-ray CT by the addition of computer generated statistical noise with spatial correlation, and that this simple method can be used in other X-ray procedures where there is significant spatial correlation of noise.
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Acknowledgments
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Thanks to the radiographic staff who carried out the imaging, and to the ImPACT group at St George's Hospital for use of computing facilities.
Received for publication April 30, 2003.
Revision received August 12, 2003.
Accepted for publication September 24, 2003.
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References
|
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- Hughes JS, O'Riordan MC. Radiation exposure to the UK population: 1993 review. Oxon, England: National Radiation Protection Board, 1993.
- Haaga JR, Miraldi F, MacIntyre W, LiPuma JP, Bryan PJ, Wiesen E. The effect of mAs variation upon computed tomography image quality as evaluated by in vivo and in vitro studies. Radiology 1981;138:449–54.[Abstract/Free Full Text]
- Naidich DP, Marshall CH, Gribbin C, Arams RS, McCauley DI. Low dose CT of the lungs: preliminary observations. Radiology 1990;175:729–31.[Abstract/Free Full Text]
- Mayo JR, Hartman TE, Lee KS, Primack SL, Vedal S, Muller NL. CT of the chest: minimal tube current required for good image quality with the least radiation does. AJR Am J Roentgenol 1995;164:603–7.[Abstract/Free Full Text]
- Lee SY, Primack SL, Staples CA, Mayo JR, Aldrich JE, Muller NL. Chronic infiltrative lung disease: comparison of diagnostic accuracies of radiography and low and conventional dose thin section CT. Radiology 1994;191:669–73.[Abstract/Free Full Text]
- Ravenel JG, Scalzetti EM, Huda W, Garrisi W. Radiation exposure and image quality in chest CT examinations. AJR Am J Roentgenol 2001;177:279–84.[Abstract/Free Full Text]
- Trefler M, Haughton V. Patient dose and image quality on computed tomography. AJR Am J Roentgenol 1981;137:25–7.[Abstract/Free Full Text]
- Mayo JR, Whittall KP, Leung AN, Hartman TE, Park CS, Primack SL, et al. Simulated dose reduction in conventional chest CT: validation study. Radiology 1997;202:453–7.[Abstract/Free Full Text]
- Frush DP, Slack CC, Hollingsworth CL, Bissett GS, Donnelly LF, Hsieh J, et al. Computer-simulated radiation dose reduction for abdominal CT of pediatric patients. AJR Am J Roentgenol 2002;179:1107–13.[Abstract/Free Full Text]
- Riederer SJ, Pelc NJ, Chesler DA. The noise power spectrum in computed X-ray tomography. Phys Med Biol 1978;23:446–54.[CrossRef][Medline]
- Evans AL. The evaluation of medical images. Bristol: Adam Hilger 1981;32–41.
- Bogartz G, Golding SJ, Jurik AG, Leonardi M, Van Meerten EvP, Geleijns K, et al. European guidelines on quality criteria for computed tomography. Eur 16262 EN.
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Abstract
Introduction
