chen aapm 2017 handoutamos3.aapm.org/abstracts/pdf/127-35389-418554-125540...0.05 0.1 0.15 0.2 0.25...

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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



¡ Low dose CT software method (2):Combination of denoising and modeling of photon statistics in model based image reconstruction (MBIR);


¡ 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

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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


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


σ2 (H

U2 )

1 mGy5 mGy20 mGy60 mGy

Noise variance is inversely proportional to the cubic of Δx

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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)

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¡ Low dose CT software method (2):Combination of denoising and photon statistics modeling in model based image reconstruction (MBIR);


¡ 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

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¡ 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)





¡ Summary

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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

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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.





¡ Summary

Question: How would our cheat sheet change when a nonlinear model based iterative reconstruction or other nonlinear denoising technique is used?

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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 ∝


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


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


0.625 1.25 2.5 5101

102

103


σ2 (H

U2 )

FBPVeo 2 1

zσ ∝

Δ

2 1z

σ ∝Δ

FBP:

MBIR:



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


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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)


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

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¡ 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.

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