Nuclear Medicine
Effect of Overlapping Projections on Reconstruction Image Quality in
Multipinhole SPECT
Kathleen Vunckx
Johan Nuyts
Nuclear Medicine, K.U.Leuven
Nuclear Medicine
Outline
• Introduction
• Pinhole design evaluation method
• Effect overlap
• Conclusions and future work
Nuclear Medicine
Pinhole SPECT
Clinical SPECT camera
Pinhole collimator
Pinhole insert
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
Nuclear Medicine
Single vs. multipinhole SPECT
Nuclear Medicine
Single vs. multipinhole SPECT
• Improved sensitivity• Better sampling
Higher reconstructio
n image quality
Nuclear Medicine
Outline
• Introduction
• Pinhole design evaluation method
• Effect overlap
• Conclusions and future work
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
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
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)
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
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
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
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:
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
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
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
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
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~
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~
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!
Nuclear Medicine
Pinhole design evaluation method: validation study
we
eks
hours
Nuclear Medicine
Outline
• Introduction
• Pinhole design evaluation method
• Effect overlap
• Conclusions and future work
Nuclear Medicine
Collimator
Detector
Collimator
Detector
Overlapping projections:problem statement
OVERLAP NO OVERLAP
Extra shielding
Nuclear Medicine
Collimator
Detector
Collimator
Detector
Overlapping projections:benificial?
Higher sensitivity
OR Unambiguous information
OVERLAP NO OVERLAP
Extra shielding
Nuclear Medicine
Overlapping projections:benificial?
105 15
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
Nuclear Medicine
Outline
• Introduction
• Pinhole design evaluation method
• Effect overlap
• Conclusions and future work
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
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
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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