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8/10/17
1
Guang-Hong Chen PhD
Professor of Medical Physics and Radiology
2
R01 CA 169331R01 EB020521U01 EB021183
Patent royalties received from GE Healthcare
¡ Scientific foundation of radiation dose reduction;¡ Low dose CT software method (1):
Combination of denoising and the conventional filtered backprojection (FBP) reconstruction;
¡ Low dose CT software method (2):Combination of denoising and modeling of photon statistics in model based image reconstruction (MBIR);
¡ Challenges and opportunities in low dose CT software technologies
¡ Summary
¡ Scientific foundation of radiation dose reduction;¡ Low dose CT software method (1):
Combination of denoising and the conventional filtered backprojection (FBP) reconstruction;
¡ Low dose CT software method (2):Combination of denoising and modeling of photon statistics in model based image reconstruction (MBIR);
¡ Challenges and opportunities in low dose CT software technologies
¡ Summary
ALARA1,2 principle: reduce radiation dose as low as it is reasonably achievable such that diagnostic performance is
not compromised!
1 ICRP, Publication 87 (2000) 2 J. R. Haaga, Am J Roentgenol, (2001)
¡ Signal quantificationSignal amplitude: CT Number and integration over a finite size areaSignal blurring: Point Spread Function (PSF) and modulation transfer function (MTF)
¡ Noise quantificationNoise amplitude: Noise varianceNoise power: Noise Power Spectrum (NPS)
¡ Overall performance quantificationContrast-to-noise ratio (CNR)Task-based detectability index (d’)2
8/10/17
2
Task-based detectability (ideal observer): 𝑑" # = ∫ d𝐤|T 𝐤 MTF(𝐤)|#
NPS(𝐤)
mA
kV
Rotation time
PitchSlice
Thickness SFOV
DFOV
Recon method
etc.
ConstraintsDiagnostic imaging task
(d’)2
2( ') secd ∝
2( ') thicknessd ∝
2 2( ') (size)d ∝ 2 2( ') (contrast)d ∝
2( ') mAd ∝
𝑑" # = ∫𝑑𝐤|𝑇 𝐤 𝑀𝑇𝐹 𝐤 |#
𝑁𝑃𝑆 𝐤=1𝜎#∫𝑑𝐤 𝑇 𝐤 𝑀𝑇𝐹 𝐤 # =
𝑆#
𝜎#= 𝐶𝑁𝑅#
Under the prewhitening condition, NPS is considered to be “white”. This assumption helps reduce the detectability index to the more commonly used concept of CNR= :
Since signal level does not change too much with scanning parameters except the tube potential, one can cheat a bit by studying noise variance and spatial resolution separately to assess “image quality/performance”.
Cautions must be taken to avoid overly extrapolating conclusions. 1 Burgess, JOSA (1999)
mA
kV
Rotation time
PitchSlice
Thickness SFOV
DFOV
Recon method
etc.
ConstraintsDiagnostic imaging task
𝜎#
∝ 𝑓@ABCD×1
𝐷𝑂𝑆𝐸 ×1
𝑒JKL×
1Δ𝑥 OΔ𝑧
Simplified cheat sheet to develop low dose CT techniques!-1.5 -1 -0.5 0 0.5 1 1.5
0
0.05
0.1
0.15
0.2
0.25
Position (mm)
Poin
t Spr
ead
Func
tion
30 HU60 HU100 HU225 HU
-1.5 -1 -0.5 0 0.5 1 1.50
0.05
0.1
0.15
0.2
0.25
Position (mm)
Poin
t Spr
ead
Func
tion
16 mGy12 mGy8 mGy4 mGy
Spatial resolution is independent of dose and contrast.Dose independence Contrast independence
Li, Garrett, Ge, Chen, Med. Phys. 41, 071911 (2014)
1 2.5 5 10 20 40 60102
103
104
Dose (mGy)
σ2 (H
U2 )
¡ Noise variance (σ2) or noise standard deviation (σ)
2 2
1
1 ( )1
N
iix x
Nσ
=
= −− ∑
K. Li, J . Tang, G.-H. Chen, Med. Phys . 41, 041906 (2014)
1 2.5 5 10 20 40 60102
103
104
Dose (mGy)
σ2 (H
U2 )
2 1Dose
σ ∝
1 mGy 10 mGy 60 mGy
1 mGy 10 mGy 60 mGy
0.625 1.25 2.5 5
25
100
400
1600
6400
Slice thickness (mm)
σ2 (H
U2 )
0.625 1.25 2.5 5
25
100
400
1600
6400
Slice thickness (mm)
σ2 (H
U2 )
2 1z
σ ∝Δ
Noise variance is inversely proportional to the slice thickness.
1/ΔX
𝜎# ∝1Δ𝑥 O
𝜎#(HU#)
0.625 1.25 2.5 5
25
100
400
1600
6400
Slice thickness (mm)
σ2 (H
U2 )
1 mGy5 mGy20 mGy60 mGy
Noise variance is inversely proportional to the cubic of Δx
8/10/17
3
2 exp( )DoseuL
σ α=
Patient Size L (mm)
Dose
(m
Gy)
Szczykutowicz, T. P., Bour, R. K., Pozniak, M., & Ranallo, F. N. Journal of Applied Clinical Medical Physics, 16, 2 (2015)
2Dose exp( )uLασ
=
0 0.2 0.4 0.6 0.80
0.5
1
1.5
2
2.5
fxy (mm-1)
Nor
mal
ized
NPS
(A.U
.)
Normalized NPS (FBP)
0 0.2 0.4 0.6 0.80
2000
4000
6000
8000
10000
12000
fxy (mm-1)
NPS
(HU2 m
m2 )
NPS (FBP)5 mAs12.5 mAs25 mAs50 mAs100 mAs200 mAs300 mAs
Dose scale invariance: The shape of the NPS is independent of radiation dose!
K. L i , J . Tang, G.-H. Chen, Med. Phy s . 41 , 041906 (2014)
CNR Dose∝
0 1 2 3 40
5
10
15
20
25
CNR
R2 = 0.994
Dose
CNR
0 1 2 30
100
200
300
400
500
600
Dose (mGy)
d'2
PCD EID
(𝐝′)𝟐 ∝ 𝐃𝐨𝐬𝐞Secret sauce in NEW low dose CT software technologies:
Develop softw are technologi es to modify the func tionaldependence of either detectability or noise variance on the CTscanning parameters.
Is low dose CT software technology all about noise reduction?
Well, noise reduction plus preserving image edges for the sake of spatial resolution.
But is that all?
50% of Reference dose33% of Reference dose25% of Reference dose
18
Reference dose
?
Gomez-Cardo na et al, SPIE (2017)
8/10/17
4
¡ Scientific foundation of radiation dose reduction;¡ Low dose CT software method (1):
Combination of denoising and the conventional filtered backprojection (FBP) reconstruction;
¡ Low dose CT software method (2):Combination of denoising and photon statistics modeling in model based image reconstruction (MBIR);
¡ Challenges and opportunities in low dose CT software technologies
¡ Summary
¡ CT system hardware improvements§ Quantum and geometrical detector efficiency1,2
§ Modification of pre- and post-patient collimators3
§ Development of patient-oriented beam shaping filters (e.g. bowtie filters)4
§ Incorporation of angular and longitudinal tube current modulation5
§ Optimization of tube potential control6
20
5 M. K. Kal ra, e t. a l ., Radio logy (2004)6 L . Yu, e t. a l ., Radiographic s (2011)7 Y. J . Suh, e t. a l ., Radio logy (2013)
Software advances need to be in synergy with hardware advances to achieve improved imaging performance at
low dose levels 1 W. C. Barber, e t. a l ., Proc SPIE (2009)2 L . M. Hamberg, e t. a l ., Radio logy , (2003)3 G. Vogtmeier, e t. a l ., Proc SPIE (2008)4 N. Mai l , e t. a l ., Med Phy s (2009)
21
¡ There is a wide spectrum of software approaches that aim to enable low dose CT, some of them are:
§ Analytical reconstruction methods + denoising▪ FBP + Image domain post-processing ▪ Log-transform domain denois ing + FBP▪ Raw data domain denois ing + FBP
§ Model based Iterative reconstruction (MBIR) methods▪ Statistical model▪ Noise suppression regularizer model (denois ing process)
Image domain denoising?
22
25% of Reference dose
Image domain denois ing can be challenging when severe noise streaks are present and anatomical structures are already highly distorted 1
1 H. Zhang, e t.a l ., Med Phy s (2017)
23
25% of Reference dose Log-transformed domain
Despite the success of some techniques,1,2
it is still challenging to mitigate noise streaks due to amplified variability after performing log-transform1 T. L i , e t. a l ., IEEE Trans Nuc l Sc i (2004)2 J . Wang, e t. a l ., IEEE Trans Med (2006)
25% of Reference doseReference dose
24
Raw domain?
Working directly with the measured raw data facilitatescorrection of photon-starved measurements
8/10/17
5
¡ Some examples of methods reported in the literature§ Adaptive trimmed mean filter1
§ Multi-dimensional adaptive filtering2
§ Spline-based penalized-likelihood sinogram3
§ Adaptive noise model-based bilateral filtering for streaking and noise reduction in multi-slice CT4
§ Multi-dimensional tensor-based adaptive filter5
§ Anisotropic diffusion has been shown to reduce noise while accurately localizing and preserving edge structural information6
25
2 M. Kac hel rieß, O. Watz k e, W. Kalender, Med Phy s , 28, 4 ,(2001) 3 P. J . L . Riv ière, D. M. Bi l lmi re, IEEE Trans Med Imag , 24, 1 (2005)4 L. Yu, e t. a l ., Proc . SPIE, 7622, (2010)
1 J . Hs ieh, Med Phy s , 25, 11 (1998)
5 M. Knaup, e t. a l ., Proc . SPIE, 9412 (2015)6 O. Demirk ay a, Proc SPIE (2001)
new value
Sort intensities
Window
Trim extremes
Average central values
trimmed mean
𝛼𝑊 𝛼𝑊
𝑊
• Window width, 𝑊• Trimming proportion, 𝛼
Exactly two parameters control this filter:
1 . Hs ieh, Med Phy s , 25, 11 (1998)2. Bednar and Watt, (1984)3. Dabov et a l , BM3D, IEEE (2007)
𝐼 𝑥, 𝑡 = 1+ 𝐴𝑠𝑖𝑛(𝑥 −𝑡)
𝐷𝜕#𝐼𝜕𝑥#
= −𝐴𝐷𝑠𝑖𝑛(𝑥− 𝑡)
𝜕𝐼𝜕𝑡 ≈
𝐼 𝑥 , 𝑡 + Δ𝑡 − 𝐼(𝑥, 𝑡) Δ𝑡
1D Diffusion Equation𝜕𝐼𝜕𝑡 = 𝐷
𝜕# 𝐼𝜕𝑥#
𝐼 𝑥 , 𝑡 + Δ𝑡 ≈ 𝐼 𝑥 , 𝑡 − Δ𝑡⋅ 𝐴𝐷𝑠𝑖𝑛 𝑥 − 𝑡
Two features make diffusion as a denoising
process possible
𝑥
𝐴
𝐴𝐷
The polarity of the 2nd order partial derivative is opposite that of the noise
The modulation of this term is non-expansive
𝐼 𝑥 , 𝑡+ Δ𝑡
𝜕𝐼𝜕𝑡 = 𝛻 ⋅ (𝐷 𝑥 , 𝑡 𝛻𝐼) = 𝛻𝐷 ⋅ 𝛻𝐼+ 𝐷𝛻#𝐼 𝐼 𝑥 , 𝑡 + Δ𝑡 ≈ 𝐼 𝑥 , 𝑡 + 𝛻𝐷 ⋅ 𝛻𝐼+ 𝐷𝛻#𝐼
Noisy raw counts 𝐼(𝑢, 𝑣, 𝑡 = 0)
𝛻𝐷⋅ 𝛻𝐼
𝐷𝛻# 𝐼
W= [50,550]W = [0, 1700]
W = [−3,3]
W [ 3 3]
Horizontal profilesVertical profiles
1. Perona and Malik, IEEE (1990)
§ More often used bi-lateral filters can be considered as a special case of the diffusion filter when the diffusion coefficient function, D(x,t), is selected to be a Gaussian-like function.2
29
§ The dot product term generates the desired polarity for noise cancellation already, there is no need for the Laplacian term for denoising purpose! That is perhaps one of the reasons that thisterm was dropped in the numerical implementation in the originalpaper by Perona and Malik.1
§ Numerically, the computation of higher order derivatives involvesthe average over more neighboring pixels and thus smooth imageedges more than the computation of only first order derivatives.
1. Perona and Malik, IEEE (1990)2. Barash, IEEE (2002)
¡ Scientific foundation of radiation dose reduction;¡ Low dose CT software method (1):
Combination of denoising and the conventional filtered backprojection (FBP) reconstruction;
¡ Low dose CT software method (2):Combination of denoising and photon statistics modeling in model based image reconstruction (MBIR);
¡ Challenges and opportunities in low dose CT software technologies
¡ Summary
8/10/17
6
31
€
I
€
Ik
!)(
k
II
k IIeIP
k−=
Given a single sample of stochastic measurement of x-rayphotons, the best we know is the probability of the occurrence,that is given by the Poisson statistics model
!)|}({
1 k
Ik
M
k
Ik I
IeIPk
k∏=
−=µ
Joint probability of a data set:
32
})({)()|}({}){|()|}({
i
iii NP
PNPNPNP µµµµ =⇒
What is the probability of estimating the attenuation distribution of an image object given the measured data set in your hand?
Image Reconstruction problem statement:
Seek for an estimation to maximize the probability!
Bayesian rule
¡ Maximizing the Log-likelihood function:
33
)](ln)lnln([maxarg
})]{|),(([lnmaxarg:~
1µ
µµ
µ
µ
PNNNN
NExP
iii
M
ii
i
+−+−=
=
∑=
!
¡ Under the following quadratic approximation:
)]()()(21[minarg:~ µλµµµ
µ
!!!!! RAyDAy T +−−=
},,,{ 21 MNNNdiagD !=34
)]()()(21[minarg:~ µλµµµ
µ
!!!!! RAyDAy T +−−=
)(1 kT
kk AyDPAv µµ!!!!
−+=+
⎭⎬⎫
⎩⎨⎧ +−= −++ )(||||21minarg: 2
11 1 µλµµµ
!!!! Rv Pkk
Data consistency driven image update:
Denoising:
1. Combettes and Wi js , Mul tis c a le Model . Simul ., Vol . 4 : 1168(2005)2. L i Y, Niu K, Tang J , Chen G-H. Proc . SPIE, 2014. p . 90330U-U-8.
35
𝜆 = 0.4
Denoised signalTrue signal
𝐒 𝐱𝐢 = 𝐚𝐫𝐠𝐦𝐢𝐧𝒙𝟏𝟐𝒙 − 𝒙𝒊 𝟐 +𝝀 𝒙 ,𝑺 𝒙𝒊 = �
𝒙𝒊 − 𝝀, 𝒙𝒊 ≥ 𝝀𝟎, −𝝀 < 𝒙𝒊 < 𝝀𝒙𝒊 +𝝀, 𝒙𝒊 ≤ −𝝀
Low dose CT techniques: MBIR
Final imageProjection data
Estimated image
Forward projection
Update the estimated image
8/10/17
7
37
FBP recon
MBIR
Reduce streaks caused by low photon count (high noise) projection data and reduced noise level
FBP
This Abdomen/Pevis CT scan covers ~40 cm in the z direction with a 0.7 mSv effective dose. The BMI of this patient is 19.4.
Veo
39
RED-CNNConvolutional
De-conv
ReLUDecoder
Encoder
Biomed Opt Express. 2017 Feb 1; 8(2): 679–694.
Courtesy of Dr. GE Wang
40
K-SVDNormal-dose TV-POCS
BM3D Wavelet RED-CNN
Courtesy of Dr. GE WangBiomed Opt Express. 2017 Feb 1; 8(2): 679–694.
¡ Scientific foundation of radiation dose reduction;¡ Low dose CT software method (1):
Combination of denoising and the conventional filtered backprojection (FBP) reconstruction;
¡ Low dose CT software method (2):Combination of denoising and photon statistics modeling in model based image reconstruction (MBIR);
¡ Challenges and opportunities in low dose CT software technologies
¡ Summary
Question: How would our cheat sheet change when a nonlinear model based iterative reconstruction or other nonlinear denoising technique is used?
8/10/17
8
1 2.5 5 10 20 40 60101
102
103
104
Dose (mGy)
σ2 (H
U2 )
FBPFBP (fitting)
1 2.5 5 10 20 40 60101
102
103
104
Dose (mGy)
σ2 (H
U2 )
FBPFBP (fitting)MBIR
Noise variance is inversely proportional to radiation dose
2 1Dose
σ ∝FBP:
MBIR:2σ Dose
?K. Li, J . Tang, G.-H. Chen, Med. Phys . 41, 041906 (2014)
1 2.5 5 10 20 40 60101
102
103
104
Dose (mGy)
σ2 (H
U2 )
FBPFBP (fitting)VeoVeo (fitting) 2 1
Doseσ ∝FBP:
MBIR: 20.4
1Dose
σ ∝
K. Li, J . Tang, G.-H. Chen, Med. Phys . 41, 041906 (2014)
0.625 1.25 2.5 5101
102
103
Slice thickness Δz (mm)
σ2 (H
U2 )
FBP
0.625 1.25 2.5 5101
102
103
Slice thickness Δz (mm)
σ2 (H
U2 )
FBPVeo
Matc hed W/L: 50/0; CTDIvol = 4 mGy
Veo
FBP
0.625 mm 1.25 mm 2.5 mm 5.0 mm
Noise variance is inversely proportional to slice thickness
2 1z
σ ∝Δ
K. Li, J . Tang, G.-H. Chen, Med. Phys . 41, 041906 (2014)
0.625 1.25 2.5 5101
102
103
Slice thickness Δz (mm)
σ2 (H
U2 )
FBPVeo 2 1
zσ ∝
Δ
2 1z
σ ∝Δ
FBP:
MBIR:
K. Li, J . Tang, G.-H. Chen, Med. Phys . 41, 041906 (2014)
K. Li, J . Tang, G.-H. Chen, Med. Phys . 41, 041906 (2014)
0 0.2 0.4 0.6 0.80
100
200
300
400
500
600
700
800
fxy (mm-1)
NPS
(HU
2 mm
2 )
NPS (Veo)
5 mAs12.5 mAs25 mAs50 mAs100 mAs200 mAs300 mAs
NPS of MBIR
0 0.2 0.4 0.6 0.80
1
2
3
4
5
6
fxy (mm-1)
Nor
mal
ized
NPS
(A.U
.)
Normalized NPS (Veo)
5 mAs12.5 mAs25 mAs50 mAs100 mAs200 mAs300 mAs
Normalized NPS of MBIR
The shape of the NPS independent on radiation dose
K. Li, J . Tang, G.-H. Chen, Med. Phys . 41, 041906 (2014)
8/10/17
9
peak const.f =FBP:
MBIR: ( )15
peak dosef ∝
1 2.5 5 10 20 40 600.05
0.1
0.2
0.4
0.8
Dose (mGy)
NPS
pea
k po
sitio
n f pe
ak (m
m-1
)
FBPFBP (fitting)VeoVeo (fitting)
K. Li, J . Tang, G.-H. Chen, Med. Phys . 41, 041906 (2014)
16 33 62 99 224 346 814 1710 25% 50%
75% 100%
0.2
0.4
0.6
0.8
1
DoseContrast (HU)
PSF
wid
th (m
m)
0.4
0.5
0.6
0.7
0.8Veo
FBP
16 33 62 99 224 346 814 1710 25% 50%
75% 100%
0.2
0.4
0.6
0.8
1
DoseContrast (HU)
PSF
wid
th (m
m)
0.4
0.5
0.6
0.7
0.8Veo
FBP
Widt
h of
PSF
(mm
)
(mm)
Li, Garrett, Ge, Chen, Med. Phys . 41, 071911 (2014 )
¡ Catphan® 600 phantom
¡ Acquisition parameters:§ 50 repeated scans
§ Axial acquisition§ Detector coverage: 20 mm x 0.625 mm§ Head bowtie
§ Three kV levels: 80, 100, 120§ 10 reduced mAs levels:, 4-104
§ Ground truth mAs: 1400
¡ Reconstruction parameters§ FBP and MBIR reconstruction methods
§ Slice thickness 0.625 mm§ DFOV: 22 cm 51
§ Air§ PMP§ LDPE§ Water§ Polystyrene§ Acrylic§ Delrin ®
§ Teflon ®
= 𝐂𝐓#(𝐃) − 𝐂𝐓#(𝐃𝐇𝐢𝐠𝐡 )
Bia
s (H
U)
FBP at 80 kV MBIR at 80 kV
8/10/17
10
¡ Scientific foundation of radiation dose reduction;¡ Low dose CT software method (1):
Combination of denoising and the conventional filtered backprojection (FBP) reconstruction;
¡ Low dose CT software method (2):Combination of denoising and photon statistics modeling in model based image reconstruction (MBIR);
¡ Challenges and opportunities in low dose CT software technologies
¡ Summary
¡ The conventional functional dependence of imaging performance on scanning parameters demonstrates non-linear behavior in image quality assessment;
¡ Low dose CT can be achieved by combining denoisingtechniques in the raw detector counts domain to reduce noise while suppressing photon starvation noise streaks;
¡ Low dose CT can also be iteratively achieved by incorporating noise streak suppression in the reconstruction process followed by a denoising filtration process;
¡ Low dose CT also increases CT number bias.
57
e
Email Contact: [email protected]
Acknowledgement
Special thanks to Dr. Ke Li, John Garrett, Yinsheng Li, Daniel Gomez-Cardona, and Juan Pablo Cruz-Bastida for help in preparing the slides.