Effect of Overlapping Projections on Reconstruction Image Quality in Multipinhole SPECT
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Transcript of Effect of Overlapping Projections on Reconstruction Image Quality in Multipinhole SPECT
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Nuclear Medicine
Effect of Overlapping Projections on Reconstruction Image Quality in
Multipinhole SPECT
Kathleen Vunckx
Johan Nuyts
Nuclear Medicine, K.U.Leuven
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Nuclear Medicine
Outline
• Introduction
• Pinhole design evaluation method
• Effect overlap
• Conclusions and future work
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Nuclear Medicine
Pinhole SPECT
Clinical SPECT camera
Pinhole collimator
Pinhole insert
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Nuclear Medicine
Parallel hole vs. pinhole SPECTParallel hole collimator
Pinhole collimator
Geometrical Magnification
Reduced field of view and
increased resolution
=> ideal for small animal imaging
Detector
Focal Point
Detector
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Nuclear Medicine
Single vs. multipinhole SPECT
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Nuclear Medicine
Single vs. multipinhole SPECT
• Improved sensitivity• Better sampling
Higher reconstructio
n image quality
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Nuclear Medicine
Outline
• Introduction
• Pinhole design evaluation method
• Effect overlap
• Conclusions and future work
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Nuclear Medicine
• # detectors• # pinholes/detector
• Diameter of the pinholes
• Acceptance angle (A)• Inclination angle (I)• Position of the
pinholes (PA, PD)
• Distance to detector (DD)
• Distance to AOR (DA)• Insert thickness (T)• Focussing point (F)
axis of rotation (AOR)
T
DD
DAF
PD
PAA
I
Pinhole design evaluation method: design parameters
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Nuclear Medicine
Pinhole design evaluation method: introduction
• Aim: Fast method for evaluation of various (multi)pinhole collimator designs
• Evaluation: Quantify the effect of the design on the signal and the noise of the reconstructed voxel values
Fixed target resolution!
Impulse response & covariance
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Nuclear Medicine
Pinhole design evaluation method:impulse response
Phantom/Animal
Projection data
Recon-struction
Without impulse
With impulse
Impulse response
central value & variance
contrast-to-noise ratio (CNR)
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Nuclear Medicine
Pinhole design evaluation method: reference method
Very slow, takes weeks to find a decent design!
impulse
impulsewithoutreconimpulsewithrecon .. central value
variance
• Impulse response:
• Covariance image:For each design:
For a set of voxels:Simulate a lot of iterative reconstructions with different noise on the projection data
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Nuclear Medicine
i i
ii AXy2
2
Pinhole design evaluation method: efficient analytical method
• Can we more efficiently calculate:– Impulse response– Covariance image
• Weighted least squares approximation:
AXYCAXY YT 1
reconstructed image
projection
measurement in detector pixel i
variance (= weight)
Assumes Gaussian distribution!
Matrix notation:
covariance matrix of Y
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Nuclear Medicine
Pinhole design evaluation method: efficient analytical method
• Impulse response:
ACAACAX YT
YT 111
0x
AXYCAXY YT 1min
YCAACAX YT
YT 111
AY
Weighted least squares
reconstructed image
projection
covariance matrix of Y
measurement
Impulse response in voxel j:
impulse
Fisher information
jj FFX 1
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Nuclear Medicine
TT
YT
T
YYYT
TT
Y
T
YT
T
X
FFF
FACAF
FACCCAF
FACYYYYECAF
XXXXEC
11
111
1111
1111
Pinhole design evaluation method: efficient analytical method
• Covariance matrix Cx
covariance matrix of Y
YCAFX YT 11
jTjX FFFC 11
Covariance in voxel j:
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Nuclear Medicine
Pinhole design evaluation method: efficient analytical method
• For a WLS approximation:
• For pinhole SPECT post-smoothed MLEM reconstruction:– Shift-variant
jTjX
jj
FFFC
FFX
11
1
F point 1 F point 2
12
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Nuclear Medicine
Pinhole design evaluation method: efficient analytical method
• For a WLS approximation:
• For pinhole SPECT post-smoothed MLEM reconstruction:– Shift-variant => assume local shift-invariance
=> turn F into a circulant matrix F j
jTjX
jj
FFFC
FFX
11
1
…
…
…
…row j
shifted row j
shifted row j
matrix F matrix Fj
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Nuclear Medicine
Pinhole design evaluation method: efficient analytical method
• For a WLS approximation:
• For pinhole SPECT post-smoothed MLEM reconstruction:– Shift-variant:– Local approximations
Good approximation close to voxel j, less accurate if distance from j increases
jTjX
jj
FFFC
FFX
11
1
=> multiply elements of Fj with weight that linearly descreases with increasing distance from j
jFF
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Nuclear Medicine
Pinhole design evaluation method: efficient analytical method
• For a WLS approximation:
• For pinhole SPECT post-smoothed MLEM reconstruction:– Shift-variant:– Local approximations:– Incomplete data => not of full rank
=> does not exist
jTjX
jj
FFFC
FFX
11
1
=> Replace by approximated pseudoinverse G (calculated in Fourier domain)
jj FF~
jFF
jF~
1~ jF
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Nuclear Medicine
Pinhole design evaluation method: efficient analytical method
• For a WLS approximation:
• For pinhole SPECT post-smoothed MLEM reconstruction:– Shift-variant:– Local approximations:– Incomplete data:– Post-smoothing to obtain fixed target resolution
=> for each voxel j, choose an isotropicalGaussian P such that is as
accurateas possible
jTjX
jj
FFFC
FFX
11
1
jFPGT~
isotropical Gaussian with FWHM = target resolution
jFF jj FF~
GF j 1~
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Nuclear Medicine
Pinhole design evaluation method: efficient analytical method
• For a WLS approximation:
• For pinhole SPECT post-smoothed MLEM reconstruction:– Shift-variant:– Local approximations:– Incomplete data:– Post-smoothing:
jTTjjX
jjj
PGFPGC
FPGX
~
~
jTjX
jj
FFFC
FFX
11
1
jFF jj FF~
GF j 1~
jFPGT~
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Nuclear Medicine
• Good local approximations for:– Impulse response central value– Covariance image variance
• Approximates post-smoothed MLEM with fixed target resolution
Pinhole design evaluation method: efficient analytical method
Quite efficient, takes a few hours to find a decent design!
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Nuclear Medicine
Pinhole design evaluation method: validation study
we
eks
hours
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Nuclear Medicine
Outline
• Introduction
• Pinhole design evaluation method
• Effect overlap
• Conclusions and future work
![Page 24: Effect of Overlapping Projections on Reconstruction Image Quality in Multipinhole SPECT](https://reader035.fdocuments.in/reader035/viewer/2022070406/5681427e550346895daea875/html5/thumbnails/24.jpg)
Nuclear Medicine
Collimator
Detector
Collimator
Detector
Overlapping projections:problem statement
OVERLAP NO OVERLAP
Extra shielding
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Nuclear Medicine
Collimator
Detector
Collimator
Detector
Overlapping projections:benificial?
Higher sensitivity
OR Unambiguous information
OVERLAP NO OVERLAP
Extra shielding
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Nuclear Medicine
Overlapping projections:benificial?
105 15
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Nuclear Medicine
Overlapping projections:conclusions
• With overlap– Do not use too many apertures– Pinhole apertures farther from each other
• Without overlap– More pinholes– Pinhole apertures closer to each other– Better than same design with overlap
REMOVE OVERLAP
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Nuclear Medicine
Outline
• Introduction
• Pinhole design evaluation method
• Effect overlap
• Conclusions and future work
![Page 29: Effect of Overlapping Projections on Reconstruction Image Quality in Multipinhole SPECT](https://reader035.fdocuments.in/reader035/viewer/2022070406/5681427e550346895daea875/html5/thumbnails/29.jpg)
Nuclear Medicine
Conclusions
• Accurate and efficient method to evaluate pinhole collimator designs by predicting the image reconstruction quality.
• Useful to investigate:– effect of design parameters– effect of overlapping projections
• Removing overlap gives promissing results
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Nuclear Medicine
Future work
• Optimize (dual head) multipinhole design for:– rat brain imaging– whole body mouse imaging– cardiac imaging in rabbits
• Investigate influence of multipinhole-specific artifacts
• Extend method to model collimator penetration and attenuation
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Nuclear Medicine
Effect of Overlapping Projections on Reconstruction Image Quality in
Multipinhole SPECT
Kathleen Vunckx
Johan Nuyts
Nuclear Medicine, K.U.Leuven