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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 SPECT Parallel 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 DA F PD PA A 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! 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 Pinhole design evaluation method: efficient analytical method Can we more efficiently calculate: –Impulse response –Covariance image Weighted least squares approximation: 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: Weighted least squares reconstructed image projection covariance matrix of Y measurement Impulse response in voxel j: impulse Fisher information

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Nuclear Medicine Pinhole design evaluation method: efficient analytical method Covariance matrix C x covariance matrix of Y 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 F point 1 F point 2 1 2

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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 … … … … row j shifted row j matrix Fmatrix F 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: –Local approximations Good approximation close to voxel j, less accurate if distance from j increases => multiply elements of F j with weight that linearly descreases with increasing distance from 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: –Local approximations: –Incomplete data=> not of full rank => does not exist => Replace by approximated pseudoinverse G (calculated in Fourier domain)

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

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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:

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Nuclear Medicine Good local approximations for: – Impulse responsecentral value – Covariance imagevariance 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 weeks hours

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Nuclear Medicine Outline Introduction Pinhole design evaluation method Effect overlap Conclusions and future work

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Nuclear Medicine Collimator Detector Collimator Detector Overlapping projections: problem statement OVERLAPNO OVERLAP Extra shielding

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Nuclear Medicine Collimator Detector Collimator Detector Overlapping projections: benificial? Higher sensitivity OR Unambiguous information OVERLAPNO OVERLAP Extra shielding

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Nuclear Medicine Overlapping projections: benificial? 10 5 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

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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

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Nuclear Medicine Pinhole design evaluation method: reconstruction quality quantification (Pinhole) SPECT reconstruction: –space-variant –nonlinear in the projection data Q unknown activity distribution image reconstruction projectionimpulse response mean Fessler et al. Local impulse response (LIR)

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Nuclear Medicine Pinhole design evaluation method: reconstruction quality quantification Linearized local impulse response (LLIR) Assume the reconstruction is locally linear noiseless projection data noisy projection data Fessler et al.

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Nuclear Medicine Pinhole design evaluation method: efficient analytical method Approximations for the LLIR and its covariance matrix after convergence of MAP reconstruction: Fixed target resolution to compare designs –With MAP: Stayman et al., Nuyts et al., Fessler et al. –With post-smoothed MLEM: T ≈ PGF Fessler et al.

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Nuclear Medicine Pinhole design evaluation method: efficient analytical method Assume F is local shift-invariant Turn F into a circulant matrix F j Approximated pseudoinverse G (in Fourier domain): with convolutions (in spatial domain), or products (in Fourier domain)

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