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

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Pinhole SPECT

Clinical SPECT camera

Pinhole collimator

Pinhole insert

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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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Single vs. multipinhole SPECT

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Single vs. multipinhole SPECT

• Improved sensitivity• Better sampling

Higher reconstructio

n image quality

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Outline

• Introduction

• Pinhole design evaluation method

• Effect overlap

• Conclusions and future work

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• # 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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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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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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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

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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

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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

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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

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Collimator

Detector

Collimator

Detector

Overlapping projections:benificial?

Higher sensitivity

OR Unambiguous information

OVERLAP NO OVERLAP

Extra shielding

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Overlapping projections:benificial?

105 15

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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

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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