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Abstract
This paper introduces a new strategy for simulating lowdose computed tomography (CT) scans using real scans of a higher dose as an input. The tool is verified against simulations and real scans and compared to other approaches found in the literature.
The conditional variance identity is used to properly account for the variance of the input highdose data, and a formula is derived for generating a new Poisson noise realization which has the same mean and variance as the true lowdose data. The authors also derive a formula for the inclusion of real samples of detector noise, properly scaled according to the level of the simulated xray signals.
The proposed method is shown to match real scans in number of experiments. Noise standard deviation measurements in simulated lowdose reconstructions of a 35 cm water phantom match real scans in a range from 500 to 10 mA with less than 5% error. Mean and variance of individual detector channels are shown to match closely across the detector array. Finally, the visual appearance of noise and streak artifacts is shown to match in real scans even under conditions of photonstarvation (with tube currents as low as 10 and 80 mA). Additionally, the proposed method is shown to be more accurate than previous approaches (1) in achieving the correct mean and variance in reconstructed images from purePoisson noise simulations (with no detector noise) under photonstarvation conditions, and (2) in simulating the correct noise level and detector noise artifacts in real lowdose scans.
The proposed method can accurately simulate lowdose CT data starting from highdose data, including effects from photon starvation and detector noise. This is potentially a very useful tool in helping to determine minimum dose requirements for a wide range of clinical protocols and advanced reconstruction algorithms.
The authors would like to thank Randy Luhta and Chris Vrettos for helping to describe the electronic detector noise properties and to Dave Salk and Yong Wu for helping with the scanner acquisitions.
I. INTRODUCTION
II. STATE OF THE ART
III. PROBLEM STATEMENT
IV. ALGORITHM DERIVATION
V. ELECTRONIC NOISE IN ENERGY INTEGRATING DETECTORS
VI. NUMBER OF PHOTONS
VII. COMPARISON TO OTHER METHODS
VIII. SIMULATIONS
VIII.A. Simulations without detectornoise
VIII.B. Verification of the full model
IX. DISCUSSION AND CONCLUSION
Key Topics
 Medical image noise
 104.0
 Medical imaging
 26.0
 Computed tomography
 24.0
 Photons
 23.0
 Image sensors
 21.0
Figures
This figure shows a difference between the real electronic detector noise with offsets subtracted and the random Gaussian noise with the same variance. The gain setting agrees with the Gaussian random only in the first moment.
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This figure shows a difference between the real electronic detector noise with offsets subtracted and the random Gaussian noise with the same variance. The gain setting agrees with the Gaussian random only in the first moment.
In this figure we compare frequency spectra of the 6000 samples of a real detector noise signal associated to the 417 μs integration period (left) and we compare it to a signal of 6000 Gaussian noise realization (right) with the same noise variance as the detector noise. We can see that the lower frequencies of the real detector noise are suppressed compared to the uniform spectrum of the Gaussian signal.
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In this figure we compare frequency spectra of the 6000 samples of a real detector noise signal associated to the 417 μs integration period (left) and we compare it to a signal of 6000 Gaussian noise realization (right) with the same noise variance as the detector noise. We can see that the lower frequencies of the real detector noise are suppressed compared to the uniform spectrum of the Gaussian signal.
In this figure, we see reconstructions from scans at 121 mA and integration period 138 μs of a 30 cm diameter water phantom at 100 kV. Images are 10 mm thick, they are zoomedin close to the isocenter and visualized at a window of 350 HU, centered at 25 HU. Isocenter is denoted by the white lines in each image. The image (a) comes from the real scan, the image (b) comes from our simulation which uses a real sample of detector noise, and the image (c) is another simulation, but this time we used a zeromean Gaussian signal for detector noise, with uniform variance channel to channel. Clearly, ring artifacts that are also in the real scan are correctly simulated in the center image, while the image on the right failed to reproduce the artifacts.
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In this figure, we see reconstructions from scans at 121 mA and integration period 138 μs of a 30 cm diameter water phantom at 100 kV. Images are 10 mm thick, they are zoomedin close to the isocenter and visualized at a window of 350 HU, centered at 25 HU. Isocenter is denoted by the white lines in each image. The image (a) comes from the real scan, the image (b) comes from our simulation which uses a real sample of detector noise, and the image (c) is another simulation, but this time we used a zeromean Gaussian signal for detector noise, with uniform variance channel to channel. Clearly, ring artifacts that are also in the real scan are correctly simulated in the center image, while the image on the right failed to reproduce the artifacts.
Figure shows (a) noiseless reconstruction of the phantom used in Subsection VIII A . The outer ellipse has the long axis of 350 mm and short axis of 210 mm and HU of 0. The circle at the top has diameter of 70 mm and 750 HU. Circle at the bottom has diameter of 50 mm and HU of 1000. (b) The average of 1000 reconstructions from direct noise simulations each equivalent to a 150 mA s scan. The rest of the figures represent the mean of 1000 reconstructions from Poisson simulations of 50 mA s using: (c) direct realizations and (d) method from Sec. IV . (e)–(g) Three different state of the art methods: Benson's (Ref. ^{ 6 } ), Massoumzadeh's (Refs. ^{ 9,10 } ), and Amir's (Ref. ^{ 5 } ), respectively. We consider image (c) to be the ground truth in this experiment, in order to compare low dose simulation tools to a direct Poisson method. We observe that the mean levels are correctly estimated by our method, underestimated by the methods in (e) and (g), and overestimated by the method in (f). Images are in HU, they are centered at 25 HU, and represented in window of 150 HU. The dashed horizontal line represents the profile location used in Figs. 5 and 6 .
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Figure shows (a) noiseless reconstruction of the phantom used in Subsection VIII A . The outer ellipse has the long axis of 350 mm and short axis of 210 mm and HU of 0. The circle at the top has diameter of 70 mm and 750 HU. Circle at the bottom has diameter of 50 mm and HU of 1000. (b) The average of 1000 reconstructions from direct noise simulations each equivalent to a 150 mA s scan. The rest of the figures represent the mean of 1000 reconstructions from Poisson simulations of 50 mA s using: (c) direct realizations and (d) method from Sec. IV . (e)–(g) Three different state of the art methods: Benson's (Ref. ^{ 6 } ), Massoumzadeh's (Refs. ^{ 9,10 } ), and Amir's (Ref. ^{ 5 } ), respectively. We consider image (c) to be the ground truth in this experiment, in order to compare low dose simulation tools to a direct Poisson method. We observe that the mean levels are correctly estimated by our method, underestimated by the methods in (e) and (g), and overestimated by the method in (f). Images are in HU, they are centered at 25 HU, and represented in window of 150 HU. The dashed horizontal line represents the profile location used in Figs. 5 and 6 .
Figure represents the profile mean of the central row in reconstructed volumes for direct noise simulation (full line), method from Sec. IV (labeled as “Our method”), Benson's method (Ref. ^{ 6 } ) (labeled as Method 1), Massoumzadeh's method (Refs. ^{ 9,10 } ) (labeled as Method 2), and Amir's method (Ref. ^{ 5 } ) (labeled as Method 3). Mean levels are most closely calculated by our method.
Click to view
Figure represents the profile mean of the central row in reconstructed volumes for direct noise simulation (full line), method from Sec. IV (labeled as “Our method”), Benson's method (Ref. ^{ 6 } ) (labeled as Method 1), Massoumzadeh's method (Refs. ^{ 9,10 } ) (labeled as Method 2), and Amir's method (Ref. ^{ 5 } ) (labeled as Method 3). Mean levels are most closely calculated by our method.
Like in Fig. ( 5 ) we see five profile lines, all through the middle section of the phantom, but this time we represent the noise variance from 1000 images. Noise levels of images simulated by our method are the closest to the direct simulations when compared to the other methods.
Click to view
Like in Fig. ( 5 ) we see five profile lines, all through the middle section of the phantom, but this time we represent the noise variance from 1000 images. Noise levels of images simulated by our method are the closest to the direct simulations when compared to the other methods.
These graphs represent four statistical moments of a signal of 6000 x rays through 15 cm of polyoxymethylene across one row of the detector system. The real signal is acquired at 120 kv, 431 μs, and 50 mA. The simulations are at the same current, where the input data were 100 mA. There are 672 channels. Graph on the far left shows that the mean of the simulation and real data match almost exactly. Center left graph shows that also the variance of the two signals matches quite well. Two graphs compare the skew and kurtosis of the two signals. Skew matches well, and there is a mismatch in kurtosis.
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These graphs represent four statistical moments of a signal of 6000 x rays through 15 cm of polyoxymethylene across one row of the detector system. The real signal is acquired at 120 kv, 431 μs, and 50 mA. The simulations are at the same current, where the input data were 100 mA. There are 672 channels. Graph on the far left shows that the mean of the simulation and real data match almost exactly. Center left graph shows that also the variance of the two signals matches quite well. Two graphs compare the skew and kurtosis of the two signals. Skew matches well, and there is a mismatch in kurtosis.
In this figure we illustrate that noise power spectrum in images reconstructed from our simulation matches the real scans. Graph on the left is obtained for the tube current of 250 mA, and graph on the right is obtained for the tube current of 30 mA. Integration period was 413 μs and tube voltage was 120 kV, scanned object was a circular water phantom with 35 cm diameter. Tube current for the input to the simulator was 500 mA.
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In this figure we illustrate that noise power spectrum in images reconstructed from our simulation matches the real scans. Graph on the left is obtained for the tube current of 250 mA, and graph on the right is obtained for the tube current of 30 mA. Integration period was 413 μs and tube voltage was 120 kV, scanned object was a circular water phantom with 35 cm diameter. Tube current for the input to the simulator was 500 mA.
In this figure we show reconstructed images at (a) 250 mA real data, (b) 30 mA real data, (c) 250 mA simulated data, and (d) 30 mA simulated data, so that the reader can appreciate closeness of our simulations. The same images are used in Fig. 8 for the calculation of noise power spectra and in Table I for noise variance comparison.
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In this figure we show reconstructed images at (a) 250 mA real data, (b) 30 mA real data, (c) 250 mA simulated data, and (d) 30 mA simulated data, so that the reader can appreciate closeness of our simulations. The same images are used in Fig. 8 for the calculation of noise power spectra and in Table I for noise variance comparison.
This figure represents the sinogram of the central slice in the 10 mA anthropomorphic pelvis scan used in the Sec. VIII B . The white dots represent readings in which no photons were detected. The views with such readings are considered photon starved projections.
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This figure represents the sinogram of the central slice in the 10 mA anthropomorphic pelvis scan used in the Sec. VIII B . The white dots represent readings in which no photons were detected. The views with such readings are considered photon starved projections.
This figure represents the comparison between the real scans (a) and different noise simulation algorithms: ours (b), Benson's (c), and Massoumzadeh's (d). Images are 10 mm slabs, centered at 75 HU with a window of 700 HU. Black arrows in (a) and (b) indicate detector noise manifestation in the image space, which occur when the data are photon starved.
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This figure represents the comparison between the real scans (a) and different noise simulation algorithms: ours (b), Benson's (c), and Massoumzadeh's (d). Images are 10 mm slabs, centered at 75 HU with a window of 700 HU. Black arrows in (a) and (b) indicate detector noise manifestation in the image space, which occur when the data are photon starved.
This figure represents an image from a high dose (200 mA) anthropomorphic pelvis scan used in Sec. VIII B . The image is a 10 mm slab, centered at 75 HU with a window of 700 HU.
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This figure represents an image from a high dose (200 mA) anthropomorphic pelvis scan used in Sec. VIII B . The image is a 10 mm slab, centered at 75 HU with a window of 700 HU.
This figure illustrates that it the physical effects such as scatter and beam hardening can have a subtle impact on our noise simulation tool. Image (a) is from the real scan, (b) is from the noise simulation that starts from the corrected data, and (c) is from the simulation that was corrected for the physical effects after the simulation. Noise measured in the circular ROI is slightly higher in image (c) (46 HU standard deviation) than in images (a) and (b) (36 and 37 HU standard deviation).
Click to view
This figure illustrates that it the physical effects such as scatter and beam hardening can have a subtle impact on our noise simulation tool. Image (a) is from the real scan, (b) is from the noise simulation that starts from the corrected data, and (c) is from the simulation that was corrected for the physical effects after the simulation. Noise measured in the circular ROI is slightly higher in image (c) (46 HU standard deviation) than in images (a) and (b) (36 and 37 HU standard deviation).
This figure contains reconstructions from (a) the real data set at 644 mA, (b) our simulation data at the level 80 mA, and (c) real data set at 80 mA. Tube voltage was 120 kV, integration period was 137 μs, and data which were used in reconstruction of (a) were also input for simulation tool. Images are visualized at 450 HU window and centered at 75 HU.
Click to view
This figure contains reconstructions from (a) the real data set at 644 mA, (b) our simulation data at the level 80 mA, and (c) real data set at 80 mA. Tube voltage was 120 kV, integration period was 137 μs, and data which were used in reconstruction of (a) were also input for simulation tool. Images are visualized at 450 HU window and centered at 75 HU.
Tables
Image noise in real scan and simulations.
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Image noise in real scan and simulations.
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Abstract
This paper introduces a new strategy for simulating lowdose computed tomography (CT) scans using real scans of a higher dose as an input. The tool is verified against simulations and real scans and compared to other approaches found in the literature.
The conditional variance identity is used to properly account for the variance of the input highdose data, and a formula is derived for generating a new Poisson noise realization which has the same mean and variance as the true lowdose data. The authors also derive a formula for the inclusion of real samples of detector noise, properly scaled according to the level of the simulated xray signals.
The proposed method is shown to match real scans in number of experiments. Noise standard deviation measurements in simulated lowdose reconstructions of a 35 cm water phantom match real scans in a range from 500 to 10 mA with less than 5% error. Mean and variance of individual detector channels are shown to match closely across the detector array. Finally, the visual appearance of noise and streak artifacts is shown to match in real scans even under conditions of photonstarvation (with tube currents as low as 10 and 80 mA). Additionally, the proposed method is shown to be more accurate than previous approaches (1) in achieving the correct mean and variance in reconstructed images from purePoisson noise simulations (with no detector noise) under photonstarvation conditions, and (2) in simulating the correct noise level and detector noise artifacts in real lowdose scans.
The proposed method can accurately simulate lowdose CT data starting from highdose data, including effects from photon starvation and detector noise. This is potentially a very useful tool in helping to determine minimum dose requirements for a wide range of clinical protocols and advanced reconstruction algorithms.
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