Effect of Overlapping Projections on Reconstruction Image Quality in Multipinhole SPECT

1. Effect of Overlapping Projections on Reconstruction Image Quality in Multipinhole SPECT Kathleen Vunckx Johan Nuyts Nuclear Medicine, K.U.Leuven

2. Outline • Introduction • Pinhole design evaluation method • Effect overlap • Conclusions and future work

3. Pinhole SPECT Pinhole collimator Clinical SPECT camera Pinhole insert

4. Parallel hole vs. pinhole SPECT Pinhole collimator Parallel hole collimator Focal Point Geometrical Magnification Detector Detector Reduced field of view and increased resolution => ideal for small animal imaging

5. Single vs. multipinhole SPECT

6. Single vs. multipinhole SPECT Higher reconstruction image quality • Improved sensitivity • Better sampling

7. Outline • Introduction • Pinhole design evaluation method • Effect overlap • Conclusions and future work

8. Pinhole design evaluation method: design parameters PD • # 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) I A PA axis of rotation (AOR) DA T F DD

9. Impulse response & covariance 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!

10. Pinhole design evaluation method:impulse response Without impulse Impulse response Phantom/Animal Projection data Recon-struction central value & variance With impulse contrast-to-noise ratio (CNR)

11. central value variance Pinhole design evaluation method: reference method • 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 Very slow, takes weeks to find a decent design!

12. Pinhole design evaluation method: efficient analytical method • Can we more efficiently calculate: • Impulse response • Covariance image • Weighted least squares approximation: measurement in detector pixel i Assumes Gaussian distribution! reconstructed image projection variance (= weight) Matrix notation: covariance matrix of Y

13. Pinhole design evaluation method: efficient analytical method measurement projection • Impulse response: reconstructed image Weighted least squares covariance matrix of Y impulse Fisher information Impulse response in voxel j:

14. Pinhole design evaluation method: efficient analytical method • Covariance matrix Cx covariance matrix of Y Covariance in voxel j:

15. Pinhole design evaluation method: efficient analytical method • For a WLS approximation: • For pinhole SPECT post-smoothed MLEM reconstruction: • Shift-variant 1 2 F point 2 F point 1

16. … … … … 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 matrix F matrix Fj shifted row j row j shifted row j

17. 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 => multiply elements of Fj with weight that linearly descreases with increasing distance from j

18. 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 => Replace by approximated pseudoinverse G (calculated in Fourier domain)

19. 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 isotropical Gaussian P such that is as accurate as possible isotropical Gaussian with FWHM = target resolution

20. 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:

21. Pinhole design evaluation method: efficient analytical method • Good local approximations for: • Impulse response central value • Covariance image variance • Approximates post-smoothed MLEM with fixed target resolution Quite efficient, takes a few hours to find a decent design!

22. weeks hours Pinhole design evaluation method: validation study

23. Outline • Introduction • Pinhole design evaluation method • Effect overlap • Conclusions and future work

24. Detector Detector Collimator Collimator Overlapping projections:problem statement OVERLAP NO OVERLAP Extra shielding

25. Detector Detector Collimator Collimator Overlapping projections:benificial? OVERLAP NO OVERLAP Extra shielding Higher sensitivity Unambiguous information OR

26. 10 15 Overlapping projections:benificial? 5

27. 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

28. Outline • Introduction • Pinhole design evaluation method • Effect overlap • Conclusions and future work

29. 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

30. 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

31. Effect of Overlapping Projections on Reconstruction Image Quality in Multipinhole SPECT Kathleen Vunckx Johan Nuyts Nuclear Medicine, K.U.Leuven