Fisher information-based evaluation of image quality for time-of-flight PET
description
Transcript of Fisher information-based evaluation of image quality for time-of-flight PET
Fisher information-based evaluation of image quality for time-of-flight PETKathleen Vunckx1, Lin Zhou1, Samuel Matej2,Michel Defrise3, Johan Nuyts1
1 Dept. of Nuclear Medicine, Katholieke Universiteit Leuven, Leuven, Belgium.2 Dept. of Radiology, University of Pennsylvania, Philadelphia, USA. 3 Dept. of Nuclear Medicine, Vrije Universiteit Brussel, Brussels, Belgium.
Outline
Introduction: TOF PET Aim & motivation Image quality evaluation methods Simulations & results Conclusions & future work
Introduction: TOF PET
1x2x
Conventional PET
Time-of-flight PETc
xt
c
xt 2
21
1 and
x
2
12 ttcx
2
tcx
Annihilation location:
Localization uncertainty:
Time annihilation detection:
Time resolution
2t1t
x
Introduction: TOF PET
Philips Gemini TF PET/CT
non-TOFnon-TOF
TOFTOF
CTCTSlice A Slice B
Courtesy of S. Matej et al.
Outline
Introduction: TOF PET Aim & motivation Image quality evaluation methods Simulations & results Conclusions & future work
Aim & motivation
Effect TOF information on image quality?
Influence TOF kernel accuracy on image quality?
2
tcx
Conventional PET
Time-of-flight PET
Time difference=
Extra information
x
Outline
Introduction: TOF PET Aim & motivation Image quality evaluation methods
– Tomitani’s analytical TOF gain calculation– Fisher information-based evaluation method for
TOF PET Simulations & results Conclusions & future work
Tomitani’sanalytical TOF gain calculation
Restrictions:– Only for central point(s) of a large uniform
non-attenuating disk source– For FBP-like reconstructions
3
2
min, 8 r
xabVarTOF
* Tomitani, IEEE TNS 28(6), 1981.
3
3
min,16 r
DabVar TOFnon
x
D
x
Db
Var
Var
TOF
TOFnon
66.0
2min,
min,
TOF PET* non-TOF PET**
Gain*
** Tanaka et al., Comp. Biol. Med., 1976.
2ln22
r
a
b (standard deviation FWHM)
amount of detected coincidences per cm²
resolution in reconstructed image (FWHM)
D
x
Fisher information-basedevaluation method for TOF-PET
Fisher information ACAF YT 1
projectioncovariance matrix of measurement
backprojection
Fessler et al., IEEE TIP 1996.Qi et al., IEEE TMI 2000.Vunckx et al., IEEE TMI 2008.
Efficient approximations for image quality of
post-filtered MLEM:– Linearized local impulse response (LLIR)– (Co)variance
in 1 pixel or small ROI
MLEM post-filter
Fixed target resolution
Fisher information-basedevaluation method for TOF-PET
0
1
0
Ij QLLIR
0
1
0
010
V
j QVar
0
/1
/1
/1
0
r
r
r
QLLIR IROI
0
/1
/1
/1
0
0111
0
r
r
r
Qrrr
Var VROI
pixels in ROIpixel j
Approximations for individual pixels
Approximations for ROI
with r = # pixels in ROI
due to local shift invariance
Also possible to insert TOF kernel mismatch in model
Outline
Introduction: TOF PET Aim & motivation Image quality evaluation methods Simulations & results
– Sim. 1: Tomitani versus Fisher information– Sim. 2: Attenuating ellipse– Sim. 3: Realistic thorax phantom– Sim. 4: Effect accuracy TOF kernel
Conclusions & future work
Simulation 1:Tomitani versus Fisher information
Homogeneous diskD = 35 cm
No attenuation, no scatter, no randoms, no detector resolution
Pixel size 0.2 cm FOV of 67.2 cm Target resolution 0.6 cm
FWHM x
D
Var
Var
TOF
TOFnon
66.0
D = 35.0cm
Nice agreement!
Simulation 2:Attenuating ellipse
Db
= 2
8.0
cm
Da = 43.8cm
0.4 Da
0.4
Db
Homogeneous ellipseDa= 43.8 cm, Db = 28.0 cm
No scatter, no randoms, no detector resolution
Attenuation (water) Pixel size 0.2 cm FOV of 67.2 cm Target resolution 0.6 cm
FWHM
Gain increases faster in the center!
17.85
1.45 1.75
1.25
13.9013.73
non-TOF
non-TOF
3.37
2.523.31
Simulation 3:Realistic thorax phantom
2D realistic thorax phantom No scatter, no randoms Attenuation modeled Intrinsic resolution 0.5 cm Pixel size 0.3375 cm FOV of 64.8 cm Target resolution 1.2 cm
FWHM
True activity
TOF PET variance t = 500 ps
Non-TOF PET variance
Variance improvement due to TOF information
> 5
4
012
3
> 5
4
0123
TOF PET variance t = 500 ps
Non-TOF PET variance
Variance improvement due to TOF information
Fisher information-based method
Based on recon. of 300 noisy proj. data setsTrue activity
Simulation 3:Realistic thorax phantom
Simulation 4:Effect accuracy TOF kernel
TOF kernel might not be known accuratelyEffect on image quality?
Narrower contrastWider contrast
Daube-Witherspoon, Matej et al., 2006 IEEE NSS Conf. Rec.
FWHM?
t = 300 ps
D = 27.0cm
ROI diam 1.3cm7cm
Simulation 4:Effect accuracy TOF kernel
mea
n R
OI
vari
ance
RO
I
CN
R R
OI
recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps)
Too narrowt = 150 ps
Too widet = 600 ps
Real TOF kernel t = 300 ps
pixels
po
st-
sm
oo
the
d
imp
uls
e r
es
po
ns
e
po
st-
sm
oo
the
d
imp
uls
e r
es
po
ns
e
pixels
D = 27.0cm
7cm
ROI diam 1.3cm
Target resolution 6 mm
Simulation 4:Effect accuracy TOF kernel
mea
n R
OI
vari
ance
RO
I
CN
R R
OI
recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps)
pixels
po
st-
sm
oo
the
d
imp
uls
e r
es
po
ns
e
po
st-
sm
oo
the
d
imp
uls
e r
es
po
ns
e
pixels
Too narrowt = 150 ps
Too widet = 600 ps
Real TOF kernel t = 300 ps Target resolution 6 mm
D = 27.0cm
7cm
ROI diam 1.3cm
Simulation 4:Effect accuracy TOF kernel
pixels (column coordinates)
activ
ity
Reconstructions homogeneous sphere 27 cm Real TOF kernel t = 300 ps
Recon TOF kernel FWHM t = 150 ps
Recon TOF kernel FWHM t = 300 ps
Recon TOF kernel FWHM t = 600 ps
CORRECTTOO NARROW TOO WIDE
Simulation 4:Effect accuracy TOF kernel
mea
n R
OI
recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps)
mea
n R
OI
vari
ance
RO
Iva
rian
ce R
OI
CN
R R
OI
CN
R R
OI
recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps) recon TOF kernel FWHM (ps)
Gaussian post-filter
Optimal post-filter (imposed Gaussian shape and FWHM)
(imposed target FWHM)
Outline
Introduction: TOF PET Aim & motivation Image quality evaluation methods Simulations & results Conclusions & future work
Conclusions
Gain in center increases with diameter and TOF resolution:
Gain in all pixels Slower increase in eccentric and high-
count regions
x
D
Var
Var
TOF
TOFnon
66.0
Kernel too wide:contrast contrast =
variance variance
Kernel too narrow:contrast contrast =
variance variance
Conclusions
Accurate kernel:best contrast vs.variance trade-off, best CNR
Gaussian post-filterGaussian post-filter Optimal post-filterOptimal post-filter
Flat optimum!Flat optimum!
CNR
CNR
artifacts
Future work
So far: – Design evaluation for multipinhole SPECT– Effect of overlapping projections in multipinhole
SPECT– Image quality improvement due to TOF
Also interesting:– Effect of randoms, scatter, … for TOF PET– 3D TOF PET– Rotating slat hole SPECT (Lin Zhou)