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Spatial frequency spectrum of the x-ray scatter distribution in CBCT projections
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10.1118/1.4822484
    + View Affiliations - Hide Affiliations
    Affiliations:
    1 Department of Medical Biophysics, University of Toronto, Toronto, Ontario M5G 2M9, Canada and Radiation Medicine Program, Princess Margaret Hospital, Toronto, Ontario M5G 2M9, Canada
    2 Department of Radiation Oncology (MAASTRO), GROW – School for Oncology and Developmental Biology, Maastricht University Medical Center, Maastricht 6201 BN, Netherlands and Department of Oncology, Medical Physics Unit, McGill University, Montreal, Quebec H3G 1A4, Canada
    3 Department of Medical Biophysics, University of Toronto, Toronto, Ontario M5G 2M9, Canada; Radiation Medicine Program, Princess Margaret Hospital, Toronto, Ontario M5G 2M9, Canada; Ontario Cancer Institute, Princess Margaret Hospital, Toronto, Ontario M5G 2M9, Canada; and Department of Radiation Oncology, University of Toronto, Toronto, Ontario M5G 2M9, Canada
    a) Author to whom correspondence should be addressed. Electronic mail: Gregory.Bootsma@rmp.uhn.on.ca; Telephone: 416-946-4501 (×4041).
    Med. Phys. 40, 111901 (2013); http://dx.doi.org/10.1118/1.4822484
/content/aapm/journal/medphys/40/11/10.1118/1.4822484
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/40/11/10.1118/1.4822484

Figures

Image of FIG. 1.
FIG. 1.

(a) Profile of compensator, F1, modeled after the Elekta F1 bowtie (aluminum with a center thickness of 3 mm). (b) Profile for compensator, AL16S, designed to compensate for a 16.4 cm diameter cylinder. AL16S is also composed of aluminum material with a center thickness of 1 mm and a modulation factor of 7.9.

Image of FIG. 2.
FIG. 2.

Axial (a) and sagittal (b) slices showing density values for voxelized head phantom used in the MC simulations.

Image of FIG. 3.
FIG. 3.

(a) Axial and (b) coronal slices of the density values for the voxelized pelvis phantom used in the MC simulations.

Image of FIG. 4.
FIG. 4.

(a)–(d) The normalized detector scatter distribution, S, and (e)–(h) the corresponding logarithm of the spatial frequency, F, for the 30.6 cm diameter water cylinder at ADD values of 18, 30, 44, and 56 cm.

Image of FIG. 5.
FIG. 5.

The normalized scatter distribution (a)–(c) and the corresponding logarithm of the F (d)–(f) for different bowtie filter implementations: (a) and (d) none, (b) and (e) F1, (c) and (f) AL16S.

Image of FIG. 6.
FIG. 6.

(a) Horizontal profiles along u axis (v = 0) and (b) vertical profiles along v axis (u = 0) for the spatial frequencies of S for the 30.6 cm diameter water cylinder with different compensator configurations (none, F1, and AL16S). A strong peak in the horizontal frequency component of F for the no compensator case is seen around 0.017/cm resulting from the two signal peaks in the horizontal rows of the scatter distribution seen in Fig. 5(a) . Both compensators diminish the strength of these peaks in the horizontal rows resulting in a decrease in F at the corresponding frequency values.

Image of FIG. 7.
FIG. 7.

Scatter distribution projections, S, for frontal views ( = 0°) of the pelvis (a) and (c) and head (b) and (d) phantom. Images (a) and (b) are without the use of a compensator, whereas images (c) and (d) are with a compensator. An increase in the signal intensity of S can clearly be seen at the edges of the pelvis (a) and head (b) phantom when a compensator is not used due to the increased coherent scattering contribution, when a compensator is used [(c)and (d)] these edge effects are significantly diminished.

Image of FIG. 8.
FIG. 8.

Scatter sinograms for the center row (a) and (c) and center column (b) and (d) of S for the pelvis phantom. The first row of images (a) and (b) is without a compensator and the second row (c) and (d) is with the AL16S compensator. Periodic signals can clearly be seen in the angular direction due to the ellipsoidal shape of the pelvis phantom.

Image of FIG. 9.
FIG. 9.

Scatter sinograms for the center row (a) and (c) and column (b) and (d) of S for the head phantom. The first row of images (a) and (b) is without a compensator and the second row (c) and (d) is with the AL16S compensator.

Image of FIG. 10.
FIG. 10.

(a) Central horizontal profile, (b) central vertical profile, and (c) central angular profile of S for both head and pelvis phantoms with (dashed lines) and without (solid lines) the use of the AL16S compensator.

Image of FIG. 11.
FIG. 11.

Logarithm images of F for the pelvis phantom with (a)–(c) and without (d)–(f) the use of the AL16S compensator for the three central planes (u-v, v-, and u-). A strong off axis signal with a slope of −1 cm/turn is seen in the image of the u-ω plane shown in (c) and (f), resulting from the rotationally variant shape of the phantom.

Image of FIG. 12.
FIG. 12.

Logarithm images of F for the head phantom with (a)–(c) and without (d)–(f) the use of the AL16S compensator for the three central planes (u-v, v-, and u-). Similar to the pelvis phantom an off axis frequency component is seen in the u- plane shown in (c) and (f).

Image of FIG. 13.
FIG. 13.

(a) Contour plot of the resulting RMSE values between the gold standard and the low pass filtered LPS S signals for the 30.6 cm diameter water cylinder with no compensator for a range of u and v values. The optimal cutoff values are found when u and v are 0.05 and 0.045 cm−1, respectively, resulting in a RMSE value of 6.1. The optimal value is marked with a “+” on the contour plot. (b) The resulting shape of the optimal low pass Butterworth filter in the frequency domain.

Image of FIG. 14.
FIG. 14.

LPS S projection for 30.6 cm diameter water cylinder (no compensator) (a) without and (b) with low pass filtering. The low pass filter cutoffs used in (b) are 0.065 and 0.045 cm−1 for u and v, respectively. (c) Gold standard scatter simulation S result. (d) The percent absolute error between the filtered and gold standard S signal. (e) The central horizontal profile of the gold standard, LPS, and filtered LPS S signals.

Image of FIG. 15.
FIG. 15.

(a)–(c) shows 0° S projection for the pelvis phantom for the LPS using 106 photons, low-pass filtered LPS (using optimal cutoff values), and the gold standard (>109 photons) S data. The LPS S signal uses an angular sampling rate of 1°. (d)–(f) shows the same data but in the form of a sinogram composed of the center horizontal row of S signal at each projection angle, .

Image of FIG. 16.
FIG. 16.

RMSE as a function of the angular sampling rate for each of the four phantom imaging conditions. The results using the SFW and optimal low-pass filter cutoff values are shown as squares (□) and crosses (+), respectively.

Image of FIG. 17.
FIG. 17.

Optimal low-pass filter cutoff values, (a) u, (b) v, and (c) , for the different angular sampling rates used in each of the four phantom imaging configurations. Two outliers at d = 72° and 90° were removed from the data for the pelvis phantom with the AL16S compensator. The optimization for these two points resulted in a selection of the highest value of searched (35.28 turns−1) indicating that no filtering in the angular direction is optimal for these cases.

Image of FIG. 18.
FIG. 18.

Axial slices for reconstructions of the head phantom with no compensator using (a) uncorrected (primary and scatter), (b) scatter corrected, and (c) primary only projection images. The scatter estimate used in correcting (b) comes from the Fourier filtered and interpolated LPS (106 photons) data with an angular sampling of every 24°.

Image of FIG. 19.
FIG. 19.

Horizontal profile from axial slice of each reconstruction of the head phantom. The location in the axial slice is indicated by the dashed line in Fig. 18(c) .

Tables

Generic image for table
TABLE I.

Imaging geometry and simulation parameters.

Generic image for table
TABLE II.

SFW values (in cm−1) along the horizontal and vertical (u,v) frequency directions for the 30.6 cm diameter cylinder for various ADD, compensator, and detector configurations.

Generic image for table
TABLE III.

SFW values for the pelvis and head phantom with and without the use of the AL16S.

Generic image for table
TABLE IV.

The optimal u and v values and corresponding RMSE. The RMSE for using no filter and using a filter with cutoffs selected from the SFW values are also shown for the case with the F1 and AL16S compensators and without the use of a compensator. The error reduction for using the optimal filter cutoffs is also presented.

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/content/aapm/journal/medphys/40/11/10.1118/1.4822484
2013-10-03
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spatial frequency spectrum of the x-ray scatter distribution in CBCT projections
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/40/11/10.1118/1.4822484
10.1118/1.4822484
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