HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Figures Only Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Kanal, K. M. Articles by Shuman, W. P. Search for Related Content PubMed PubMed Citation Articles by Kanal, K. M. Articles by Shuman, W. P. Social Bookmarking                      What's this? Hotlight (NEW!) What's Hotlight?

Impact of Operator-Selected Image Noise Index and Reconstruction Slice Thickness on Patient Radiation Dose in 64-MDCT

¹ All authors: Department of Radiology, University of Washington Medical Center, 1959 NE Pacific St., Box 357115, Seattle, WA 98195-7115.

Received November 17, 2006; accepted after revision February 5, 2007.

 
Address correspondence to K. M. Kanal (kkanal{at}u.washington.edu).

Abstract

Top Abstract Introduction Materials and Methods Results Discussion APPENDIX 1: Noise Index... APPENDIX 2: Noise Index... APPENDIX 3: Noise Index... References

 
OBJECTIVE. Our objective was to develop a better understanding of the complex interrelationship between image noise, reconstruction slice thickness, and patient radiation dose on a 64-MDCT scanner that uses automated tube current modulation.

MATERIALS AND METHODS. We reviewed physics theory and performed phantom dose measurements on a 64-MDCT scanner while altering operator-selectable image noise and reconstruction slice thickness.

RESULTS. Using phantom dose measurements to adjust theoretic predictions, we constructed both a spreadsheet and a graph that visually display the interrelationships between operator-selected image noise and reconstruction slice thickness and the resulting patient dose.

CONCLUSION. This table and graph may help operators understand the trade-offs when prospectively trying to minimize dose and optimize image noise for selected reconstruction slice thicknesses on this type of 64-MDCT scanner.

Keywords: CT imaging • CT technique • 64-MDCT • noise index • physics • radiation dose

Introduction

Top Abstract Introduction Materials and Methods Results Discussion APPENDIX 1: Noise Index... APPENDIX 2: Noise Index... APPENDIX 3: Noise Index... References

 
Historically in CT practice, patient radiation dose has been adjusted largely through altering scanner tube current (mA). However, with modern 16- and 64-MDCT scanners, the mA is under the control of an automated tube current modulation (ATCM) program. ATCM is a technique used to reduce overall patient dose by rapidly altering the mA up and down as the gantry rotates around the patient [1–12]. The mA modulation is determined from the attenuation and shape of scout scan projections of the patient. When ATCM is used, mA is computer-controlled and not operator-selectable. How then can the scanning settings on a modern CT scanner be adjusted to alter image quality or to produce a particularly low-dose examination (such as a chest CT of a young woman)?

One answer is to use a parameter indicative of the level of image noise (GE Healthcare, noise index [NI]) as an operator-selected variable. Changing the NI alters the range of mA over which the ATCM varies during gantry rotation to produce a selected level of average image noise. But average image noise is also dependent on the reconstruction slice thickness—from the same CT source data, thicker slice reconstructions are less noisy than thinner slice reconstructions. So when a radiologist is faced with trying to achieve either a low-noise examination or a low-dose examination on a scanner with ATCM, there are trade-offs among NI, slice thickness, and radiation dose that are complex and not necessarily intuitive.

We wanted to better understand the theoretic and actual (measured) relationships between NI and radiation dose at a given reconstruction slice thickness, between vendor-defined NI and reconstruction slice thickness at a given radiation dose, and between reconstruction slice thickness and radiation dose at a given NI. Our goal was to create two tools, a spreadsheet and a graphical display, to illustrate these complex interrelationships in a more comprehensible, visual fashion. These tools might be used by both radiologists and technologists to tailor individual CT examinations toward desired dose and image noise on an ATCM scanner. Anatomy-based ATCM was used in this study. ECG-based ATCM was not studied.

Although this investigation was undertaken on a single make and model of 64-MDCT scanner, we postulate that the methodology illustrated could be used to create similar visual graphic tools for other CT scanners.

Materials and Methods

Top Abstract Introduction Materials and Methods Results Discussion APPENDIX 1: Noise Index... APPENDIX 2: Noise Index... APPENDIX 3: Noise Index... References

 
CT Scanner
This investigation was undertaken on a 64-MDCT scanner (LightSpeed VCT, GE Healthcare). This scanner simultaneously acquires 64 slices of 0.625 mm over a 40-mm-thick region and has x-, y-, and z-axis ATCM capabilities [13]. The operator-selected NI level modulates the mA per rotation, based on the attenuation profiles from the scout projections, to achieve a predicted average statistical noise level in the images of the specified reconstruction slice thickness requested (usually 0.625 mm). The scout projections reflect density, size, and shape information about the patient. The mA is then altered during each gantry rotation to achieve the image NI selected by the operator at the selected reconstruction slice thickness. However, using the CT source data, secondary reconstructions at alternate slice thicknesses may be made, but each will have a different resulting noise level—thicker slices with less apparent noise than thinner slices.

Methodology
To create an NI, slice thickness, and dose spreadsheet (Table 1), we first reviewed theoretic relationships between NI, reconstruction slice thickness, and radiation dose and then validated those relationships with empiric measurement in a phantom scanned on this type of 64-MDCT scanner. Where discrepancies appeared between theoretic and measured values, we adjusted the theoretic values systematically based on measured results.

The horizontal rows of Table 1 are the NI values at the various available reconstruction slice thickness settings that maintain an isodose condition. The vertical columns are the NI values as radiation dose varies at a constant reconstruction slice thickness. Radiation measurements were performed using a standard 3-cm³ CT ionization chamber (10X5-3CT, Radcal Corporation) and a 32-cm-diameter polymethyl methacrylate (PMMA) body phantom for standardized volume CT dose index (CTDI_vol) [13–15] measurement. The CTDI_vol was also recorded from the CT scanner console.

NI versus reconstruction slice thickness (Table 1 horizontal row relationship): theory—The 64-MDCT LightSpeed VCT scanner acquires data using a 0.625-mm detector row width. Reconstructed slices may be thought of as a sandwich of data from multiple 0.625-mm detector rows. Based on uncorrelated noise theory [16], the signal-to-noise ratio (SNR) in any CT image should increase proportional to the square root of the number of 0.625-mm acquisition rows used to reconstruct the slice (e.g., for a reconstruction slice thickness of 5 mm, 8 x 0.625); the SNR should increase by a factor of approximately the square root of 8 compared with a reconstruction slice thickness of 0.625 mm. Thus, under an isodose condition in which all 0.625-mm acquisition rows receive the same radiation, NI decreases as the inverse square root of the number of 0.625-mm detector rows composing the reconstructed image (in the previous example, the measured noise decreases by a factor of 1 divided by the square root of 8).

NI versus reconstruction slice thickness (Table 1 horizontal row relationship): measurements—We sought to verify the relationship between NI and reconstruction slice thickness experimentally using the PMMA body phantom. On the 64-MDCT scanner, we acquired images at the longitudinal center of the ionization chamber with the following CT scanning parameters: 120 kVp; auto mA range, 100–750; time, 0.8 second; pitch, 1.375; beam collimation, 20 mm; large body scan field of view (SFOV) (large bowtie filter); chamber length, 100 mm; chamber factor,1.0; and exposure to dose conversion factor for PMMA, 0.78. Using the predicted NI, the reconstruction slice thickness was varied and the radiation exposure measured from which CTDI_vol was calculated. The console-displayed CTDI_vol was also recorded. The combinations of predicted NI and reconstruction slice thickness, which were varied at the console for each radiation dose measurement, were 40.0 at 0.625 mm, 28.3 at 1.25 mm, 20.0 at 2.5 mm, 16.3 at 3.75 mm, and 14.1 at 5 mm. A region of interest (ROI) of approximately 1,400 mm² was used to record the image noise or SD at the 12-, 3-, 6-, and 9-o'clock positions and the center of the phantom. The center ROI SD reading was much higher than the peripheral readings in the phantom and was omitted when calculating the average image noise. This was due to X-ray beam attenuation because the X-ray beam traveled from the periphery to the center of the phantom, giving rise to a reduction in relative photon fluence and thus an increase in the image noise or SD reading.

View larger version (16K): [in this window] [in a new window] [as a PowerPoint slide]   Fig. 1 —Representation of noise index (NI) versus reconstruction slice thickness. CT profile data are acquired using 0.625-mm detector widths and reconstructed to 0.625-, 1.25-, 2.5-, 3.75-, and 5-mm slice thicknesses. Even though reconstruction slice thickness may vary, any slice thickness is generated from acquired 0.625-mm profile data. Thus, NI for any reconstruction slice thickness can be related back to NI for reconstructed 0.625-mm slice. For instance, NI = 40 at 0.625 mm equates nearly to NI = 33.8 at 1.25 mm and NI = 15.3 at 5 mm, each having same noise level () in acquired 0.625-mm profile data, though manifesting as different measured noise levels in reconstructed slices. ROI = region of interest.

To further validate the predicted NI values, we performed several secondary (postacquisition) image reconstructions of our original acquisition rows (NI = 40, reconstruction at a slice thickness of 0.625) by changing the reconstruction slice thickness from 0.625 mm to 1.25, 2.5, 3.75, and 5 mm. The same technique was used to measure image noise and to calculate average image noise.

NI versus radiation dose (Table 1 vertical column relationship): theory—Based on Poisson statistics [14], the NI is proportional to the inverse square root of the dose. Thus, as NI is decreased to reduce the noise in an image, the radiation dose must increase. It also follows from Poisson statistics that the radiation dose increases by a factor of 10.8% for a decrease in the NI of 5% and decreases by a factor of 9.3% for an increase in the NI of 5% (Appendix 1).

NI versus radiation dose (Table 1 vertical column relationship): measurements—We verified the Poisson statistics relationship experimentally between NI and radiation dose using the PMMA body phantom to acquire images centered along the ionization chamber with the scanning parameters described previously. Using a reconstruction slice thickness of 0.625 mm, radiation exposure measurements were made at NI = 28.3, 33.8, 40.0, and 50.0. The console-displayed CTDI_vol was also recorded for each NI. The same technique described previously was used to measure image noise and to calculate average image noise.

Results

Top Abstract Introduction Materials and Methods Results Discussion APPENDIX 1: Noise Index... APPENDIX 2: Noise Index... APPENDIX 3: Noise Index... References

 
NI Versus Reconstruction Slice Thickness (Table 1 Horizontal Row Relationship)
In analyzing the CTDI phantom experiment results, we found some variance from the assumptions made from the theoretic model. We hypothesize that this minor variation arose from the vendor-specific image reconstruction algorithm. Another possible reason for the discrepancy could be the potential inhomogeneity in radiation dose among detector rows due to tube wobble and other sources of motion. We thus empirically determined the Table 1 row values at isodose (same CTDI_vol) (Appendix 2). Calculating the normalized deviation between the predicted and measured radiation doses at a specified scaled NI, we found a variation of 6.5% ± 3.9% at constant radiation dose as the reconstruction slice thickness is altered from 1.25 to 5 mm.

To validate the scaled predicted NI values, we first reconstructed the original image (NI, 40; reconstruction slice thickness, 0.625 mm) with secondary reconstruction slice thicknesses of 1.25, 2.5, 3.75, and 5.0 mm and then measured the image noise level using an ROI. The measured image noise level was next compared with the predicted NI values for the different reconstruction slice thicknesses by calculating the normalized deviation between predicted NI (at a specified radiation dose and reconstruction slice thickness) and measured NI. The average of the percentage difference between the predicted NI and measured image noise level values was within 0.6% ± 0.7% across all the reconstruction slice thicknesses—which validated the predicted NI values.

NI Versus Radiation Dose (Table 1 Vertical Column Relationship)
Theoretically, based on Poisson statistics, the radiation dose increases by a factor of 10.8% with a decrease in the NI of 5% and decreases by a factor of 9.3% with an increase in the NI of 5% (Appendix 1). We verified this relationship experimentally and found it to hold to within –0.01% ± 0.39% by calculating the normalized difference between the predicted radiation dose at a specified noise level and the measured radiation dose over all specified NIs used.

Development of an NI Table
Based on the experimental data discussed, we generated an NI table for the 64-MDCT LightSpeed VCT scanner (Table 1). This table shows the relationship between NI, reconstruction slice thickness, and relative radiation dose at a fixed pitch. The NI values for the rows were empirically determined by experiment to maintain an isodose condition. The NI values for the columns were calculated from the relationship between NI and radiation dose based on Poisson statistics. For Table 1, the relative dose of unity is set for an NI of 40 and 0.625-mm reconstruction slice thickness and acts as a seed value for all the other NI values in the table. There is no reason why this value cannot be changed, for example to 30, because all other NI values in the table would propagate throughout the table based on this change.

Because the delivered dose is affected by the NI value selected and NI also varies with reconstruction slice thickness, the appropriate selection of NI can have a major impact on delivered dose. The NI table may be used to determine how the dose changes as a function of NI at constant reconstruction slice thickness and vice versa. NI values are read down the columns and matched up for each isodose row with the Relative Dose column and Dose Difference (%) column values to obtain the difference in dose caused by a specific change in NI (Appendix 3).

The NI table does not necessarily make it easy to conceptually understand the trade-offs between the different table variables. For this reason, we reportrayed the data as a graph (Fig. 2A). On the graph, the NI values from the table are plotted on the y-axis and the relative radiation dose values from the table are plotted on the x-axis as a function of the varying reconstruction slice thickness values (plotted curves) ranging from 0.625 to 5 mm.

View larger version (17K): [in this window] [in a new window] [as a PowerPoint slide]   Fig. 2A —Graphs of noise index (NI) data from Table 1. NI data plotted versus relative dose for five reconstruction slice thicknesses: 0.625 (black), 1.25 (red), 2.5 (blue), 3.75 (brown), and 5.0 mm (green). NI graph of overall results. NI values are plotted on y-axis and relative radiation dose values are plotted on x-axis as function of varying reconstruction slice thickness values, ranging from 0.625 to 5 mm.

Top Abstract Introduction Materials and Methods Results Discussion APPENDIX 1: Noise Index... APPENDIX 2: Noise Index... APPENDIX 3: Noise Index... References

As MDCT scanners with ATCM have become available, adjustment of operator-selected noise level in the image has become more important when trying to reach the as-low-as-reasonably-achievable (ALARA) dose. This means that radiologists need to understand how noise level and reconstruction slice thickness are related to radiation dose in an environment of ATCM. This study was designed to better understand these relationships and use this understanding to create a table and a graph that could be used as tools to help deal with the trade-offs involved when selecting among these scanning parameters.

In Table 1, only the relative dose is given. In part, this is because it is easier to discuss the relative merits of various choices of NI using the normalized table. Additionally, relative dose is displayed because the CTDI_vol or dose–length product (DLP) [13–15] may change from examination type to examination type and patient to patient based on body habitus because of the scanning length and the particular bowtie filter used. This variation can be corrected by using the table. Any specific value of CTDI_vol or DLP may be placed in the table at the seed dose location. Automatic spreadsheet cell projection within the table will then yield the specific values of CTDI_vol or DLP.

We have found the NI graph a more useful tool in understanding the trade-offs among NI, slice thickness, and radiation dose. In addition to assisting radiologists and technologists in selecting scanning parameters, the graph also illustrates that lack of attention to these operator-selectable parameters could result in a substantial increase in delivered dose. For example, how much is the dose increase if NI is decreased from 40 to 30 by the operator at a constant 0.625-mm reconstruction slice thickness? Figure 2B shows the relative dose at NI of 40 and 0.625 mm reconstruction slice thickness is 1.0 (dotted line). At the same reconstruction slice thickness of 0.625 mm but changing the NI to 30, the relative radiation dose is now 1.8 (solid line)—an 80% increase in delivered dose.

View larger version (18K): [in this window] [in a new window] [as a PowerPoint slide]   Fig. 2B —Graphs of noise index (NI) data from Table 1. NI data plotted versus relative dose for five reconstruction slice thicknesses: 0.625 (black), 1.25 (red), 2.5 (blue), 3.75 (brown), and 5.0 mm (green). NI graph shows dose penalty if NI is decreased from 40 to 30 for 0.625-mm reconstruction slice thickness. As seen in graph, relative dose at NI of 40 and 0.625-mm reconstruction slice thickness is 1.0 (dotted line). At same reconstruction slice thickness of 0.625 mm, but changing NI to 30, relative radiation dose is 1.8 (solid line), resulting in 80% increase in relative dose.

View larger version (18K): [in this window] [in a new window] [as a PowerPoint slide]   Fig. 2C —Graphs of noise index (NI) data from Table 1. NI data plotted versus relative dose for five reconstruction slice thicknesses: 0.625 (black), 1.25 (red), 2.5 (blue), 3.75 (brown), and 5.0 mm (green). NI graph shows how to maintain constant radiation dose as reconstruction slice thickness is changed. For operator-selected 5-mm reconstruction slice thickness and NI of 12, how would NI change if reconstruction slice thickness was modified to 0.625 mm while maintaining same radiation dose? It can be seen that for NI of 12 and 5-mm reconstruction slice thickness, maintaining same relative radiation dose of 1.7 (dotted line) when changing to reconstruction slice thickness of 0.625 mm (solid line) requires change in NI from 12 to 31.

View larger version (18K): [in this window] [in a new window] [as a PowerPoint slide]   Fig. 2D —Graphs of noise index (NI) data from Table 1. NI data plotted versus relative dose for five reconstruction slice thicknesses: 0.625 (black), 1.25 (red), 2.5 (blue), 3.75 (brown), and 5.0 mm (green). NI graph illustrates importance of increase in relative radiation dose when reconstruction slice thickness is changed without changing NI. What happens to dose if same NI of 20 is kept when changing reconstruction slice thickness from 5 to 0.625 mm? At NI of 20 and reconstruction slice thickness of 5 mm, relative radiation dose is 0.6 (dotted line). At same NI of 20 but changing reconstruction slice thickness to 0.625 mm, relative radiation dose changes to 4.0 (solid line), thereby increasing dose by factor of 6.7 times, if maximum mA has not been reached.

APPENDIX 1: Noise Index Versus Radiation Dose

Top Abstract Introduction Materials and Methods Results Discussion APPENDIX 1: Noise Index... APPENDIX 2: Noise Index... APPENDIX 3: Noise Index... References

 
With Poisson statistics we have the following relationship [14]: N between the SD of the photon count () measured, for a specified number of X-ray photons (N) per unit volume (voxel), which may be thought of as proportional to the radiation dose (D) deposited within that voxel. What is actually measured on the CT scanner console in an image region-of-interest (ROI) leading to assignment of the noise index (NI) is the relative noise (noise as perceived by a human observer in an image [14]), which is defined by:

(1)

Note: NI is inversely proportional to D; thus, as NI increases, the dose decreases and the image noise increases.

Let a second specified operating point be selected such that the NI is increased by a certain fraction (), for example, for a 5% increase (1 + = 1.05): NI =1.05x NI. Also, (NI / NI), the fractional change in NI, may now defined as:

(2)

which is reasonable based on the definition of above.

The question now is for such a change in NI (NI), by how much does the radiation dose change (D)? We have NI =(1+ )x NI, and through substitution (equation 1):

(3)

Squaring both sides and reordering, we find:

(4)

and D is simply:

(5)

so that:

(6)

NI may either be increased ( positive) or decreased ( negative). Any value of may be used in either equation to calculate the fractional change in dose: (D / D) as a function of the fractional change in NI, that is, (NI / NI)= . Substituting = 5% in equation 6 shows that a 5% increase in NI decreases the radiation dose by a factor of 9.3%, and a 5% decrease in NI increases the radiation dose by a factor of 10.8%, as stated in the article.

APPENDIX 2: Noise Index Versus Reconstruction Slice Thickness

Top Abstract Introduction Materials and Methods Results Discussion APPENDIX 1: Noise Index... APPENDIX 2: Noise Index... APPENDIX 3: Noise Index... References

 
As mentioned in the text, our results showed some variance from the assumptions made from the theoretic model. We thus empirically determined the noise index (NI) table row values at isodose (same standardized volume CT dose index [CTDI_vol]) as shown below.

Taking the relationships:

(1)

from Appendix 1 and rearranging, we find:

(2)

which can be further rearranged into:

(3)

For the NI table horizontal row relationship, we empirically determined the NI table row values at isodose using equation 3 in this appendix. So substituting the CTDI_vol values for different NI values used in the first experiment, for example, NI = 28.3 and CTDI_vol = 62.4 mGy, NI = 20 and CTDI_vol = 60.0 mGy into this equation and scaling with the initial seed values of NI = 40, CTDI_vol = 43.7 mGy, we get the new scaled values for NI:

(4)

Similarly, for NI = 16.3, scaled NI value = 18.5; and for NI = 14.1, scaled NI value = 15.3.

APPENDIX 3: Noise Index Table

Top Abstract Introduction Materials and Methods Results Discussion APPENDIX 1: Noise Index... APPENDIX 2: Noise Index... APPENDIX 3: Noise Index... References

 
The noise index (NI) table (Table 1) may be used to determine how dose changes as a function of NI at constant reconstruction slice thickness and vice versa. NI values are read down the columns and matched up for each isodose row with the Relative Dose column and Dose Difference (%) column values to obtain the difference in dose caused by a specific change in NI. For example, from Table 1, if NI is changed from 40 to 27.9 at a slice thickness of 0.625 mm, the relative dose changes from 100% to 205%, a difference of 105%, calculated as (2.051 – 1.0) / 1.0 = 1.051 or 105%.

Acknowledgments
 
We thank Mario Ramos, lead CT technologist in the Department of Radiology at the University of Washington, and Steve Kohlmeyer from GE Healthcare for their contributions to this work.

References

Top Abstract Introduction Materials and Methods Results Discussion APPENDIX 1: Noise Index... APPENDIX 2: Noise Index... APPENDIX 3: Noise Index... References

 

1. Kalra MK, Maher MM, Toth TL, et al. Techniques and applications of automatic tube current modulation for CT. Radiology2004; 233:649 -657[Abstract/Free Full Text]
2. Kalra MK, Maher MM, Saini S. Radiation exposure and projected risks with multidetector-row computed tomography scanning: clinical strategies and technologic developments for dose reduction. J Comput Assist Tomogr 2004; 28[suppl 1]:S46 -S49[CrossRef][Medline]
3. Kalra MK, Maher MM, Hamberg L, et al. Strategies for CT radiation dose optimization. Radiology 2004;230 : 619-628[Abstract/Free Full Text]
4. Mastora I, Remy-Jardin M, Delannoy V, et al. Multi-detector row spiral CT angiography of the thoracic outlet: dose reduction with anatomically adapted online tube current modulation and preset dose savings. Radiology 2004;230 : 116-124[Abstract/Free Full Text]
5. Sigal-Cinqualbre AB, Hennequin R, Abada HT, et al. Low-kilovoltage multi-detector row chest CT in adults: feasibility and effect on image quality and iodine dose. Radiology 2004;231 : 169-174[Abstract/Free Full Text]
6. Tack D, De Maertelaer V, Gevenois PA. Dose reduction in multidetector CT using attenuation-based online tube current modulation. AJR 2003; 181:331 -334[Abstract/Free Full Text]
7. Hamberg LM, Rhea JT, Hunter GJ, et al. Multi-detector row CT: radiation dose characteristics. Radiology2003; 226:762 -772[Abstract/Free Full Text]
8. Greess H, Nömayr A, Wolf H, et al. Dose reduction in CT examination of children by an attenuation-based on-line modulation of tube current (CARE Dose). Eur Radiol 2002;12 : 1571-1576[CrossRef][Medline]
9. Greess H, Wolf H, Baum U, et al. Dose reduction in computed tomography by attenuation-based on-line modulation of tube current: evaluation of six anatomical regions. Eur Radiol2000; 10:391 -394[CrossRef][Medline]
10. Kalendar WA, Wolf H, Suess C, et al. Dose reduction in CT by on-online tube current control: principles and validation on phantoms and cadavers. Eur Radiol 1999;9 : 323-328[CrossRef][Medline]
11. Kopka L, Funke M. Anatomically adapted CT tube current: dose reduction and image quality in phantom and patient studies. (abstr) Radiology 1995;197 (P): 292
12. Jacobson DR, Foley ED, Metz S, et al. Variable milliampere CT: effect on noise and low contrast detectability. (abstr) Radiology 1996;210 (P): 326
13. [No authors listed] LightSpeed 7.X technical reference manual, direction 5116422-100, rev 2 (02/05). Waukesha, WI: GE Healthcare, 2005
14. Bushberg JT, Seibert JA, Leidholdt EM Jr, Boone JM. The essential physics of medical imaging, 2nd ed. Philadelphia, PA: Lippincott Williams & Wilkins, 2002
15. Goldman LW, Fowlkes JB. Medical CT and ultrasound: current technology and applications. In: Proceedings of the 1995 American Association of Physicists in Medicine Summer School. New London, CT: AAPM, 1995: 519-566
16. Papoulis A. Probability, random variables, and stochastic processes. New York, NY: McGraw-Hill,1965

CiteULike

Complore

Connotea

Del.icio.us

Digg

Reddit

Technorati

This Article Abstract Figures Only Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Kanal, K. M. Articles by Shuman, W. P. Search for Related Content PubMed PubMed Citation Articles by Kanal, K. M. Articles by Shuman, W. P. Social Bookmarking                      What's this? Hotlight (NEW!) What's Hotlight?