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Advanced System Models for Reconstruction in Flat-Panel Detector Cone-Beam CT

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Advanced System Models for Reconstruction in Flat-Panel Detector Cone-Beam CT Steven Tilley ([email protected]) Fully 3D Recon 2015 May 31 -June 4 Fully3D Advanced System Models for Reconstruction in Flat-Panel Detector Cone-Beam CT Steven Tilley, Jeffrey Siewerdsen, Web Stayman Department of Biomedical Engineering Johns Hopkins University Schools of Medicine and Engineering Acknowledgements AIAI Laboratory Advanced Imaging Algorithms and Instrumentation Lab aiai.jhu.edu [email protected] I-STAR Laboratory Imaging for Surgery, Therapy, and Radiology istar.jhu.edu [email protected] Faculty and Scientists Students Industry Partners Tharindu De Silva Qian Cao Sungwon Yoon Grace Gang Hao Dang Kevin Holt Aswin Mathews Sarah Ouadah David Nisius Amir Pourmorteza Sureerat Reaungamornrat Edward Shapiro Jeffrey Siewerdsen Steven Tilley II Alejandro Sisniega Ali Uneri Shiyu Xu Jennifer Xu Wojciech Zbijewski Thomas Yi Funding Supported in part by a Varian industry partnership and NIH grants R21-EB-014964 and T32-EB010021 This work was supported, in part, by the above grants. The contents of this presentation are solely the responsibility of the authors and do not necessarily represent the official view of Johns Hopkins or the NIH. The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 1 Steven Tilley ([email protected]) Fully 3D Recon 2015 May 31 -June 4 Noise model and reality mismatch Normalized Detector Units Detector Normalized Units Detector Normalized Source and Detector Blur Modeling Mean: 푔 푦 0 = 퐁푠퐃 푔 exp(−퐀휇) 푦 = 퐁푑퐁푠퐃 푔 exp(−퐀휇) Extended B B s d Source Blur X-ray Source Detector Blur 퐁 Light 퐁 푠 Photons 푑 X-ray Photons Photo- diodes Object Scintillator 푇 푇 Covariance: 퐃{푔} 퐃{푦 0} 퐁푑퐃 푦 0 퐁푑 퐁푑퐃 푦 0 퐁푑 + 퐊푟표 Uncorrelated Uncorrelated, Attenuated Correlated Light Photons Correlated Electrons Quanta: Bare Beam X-rays with Focal Spot Blur with Light Spread with Readout Noise Forward Model: 푦 (휇) = 퐁푑퐁푠퐃 푔 exp(−퐀휇) 푇 Noise Model: 푦~Gaussian(푦 , 퐊푦) 퐊풀 = 퐁푑퐃 푦 0 퐁푑 + 퐊푟표 The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 2 Steven Tilley ([email protected]) Fully 3D Recon 2015 May 31 -June 4 Linearization Simple estimate from forward model: 1 푙 = − log 퐃 퐁−1푦 푔 퐁 = 퐁푑퐁푠 Estimated Covariance of l 1 1 퐊 ≈ 퐷 퐁−1퐊 퐁−1 푇퐷 퐿 퐁−1푦 푌 퐁−1푦 Blurs may have nullspaces/regions of poor invertiblilty. 퐁−1 ≈ 퐂−1 = masked deblur 퐂 ≈ 퐂−1 −1= masked blur −1 −1 −1 푇 2 −1 푇 −1 퐊퐿 ≈ 퐷 퐂 푦 퐂 퐁푑퐷 퐂 푦 퐁푑 + 퐾휎푟표 퐂 퐷 퐂 푦 Objective Function Φ 휇 = −휓 휇 퐿 = 푙) + 훽푃(휇) Likelihood Term Penalty Term Where l is an estimate of the line integrals and µ is the attenuation values If the line integrals are from a Gaussian distribution: 푇 −1 휓 휇 퐿 = 푙) = − 퐴휇 − 푙 퐾퐿 = − A휇 − 푙 퐾퐿 퐴휇 − 푙 : weighted least squares If 푃 휇 = 휇푇푅휇 (quadratic) then: 푇 −1 −1 푇 −1 휇 = 퐴 퐾퐿 퐴 − 훽푅 퐴 퐾퐿 푙 The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 3 Steven Tilley ([email protected]) Fully 3D Recon 2015 May 31 -June 4 Solving Strategy 푇 −1 −1 푇 −1 휇 = 퐴 퐾퐿 퐴 − 훽푅 퐴 퐾퐿 푙 Preprocessing: 1 l = [− log 퐃 퐂−1푦 ] 푔 푇 −1 푏 = 퐀 퐊퐿 푙 푇 −1 Solve using CG 퐀 퐊퐿 퐀 + 훽퐑 휇 = 푏 −1 Evalulate 퐊퐿 푥: p = 퐂 푇퐷 퐂−1푦 푥 solve for q using CG where: 퐊푌푞 = 푝 푏 = 퐃 퐂−1푦 퐂 푞 return 푏 −1 −1 푇 −1 −1 퐊퐿 ≈ 퐷 퐂 푦 퐂 퐊푌 퐂 퐷 퐂 푦 Simulation Phantom Metrics: Resolution – edge response of disk Variance – spatial variance in center of disk Comparisons are made to an uncorrelated noise model: 1 퐊퐿 = −1 2 퐂 푦 + 휎푟표 Phantom: 4000x4000 25x25 µm voxels projected onto 7000 35x35 µm pixels Reconstruction: 1000x1000 100x100 µm voxels with 1750 140x140 µm pixels Geometry: SAD = 600, SDD = 1200, 720 angles, full rotation The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 4 Steven Tilley ([email protected]) Fully 3D Recon 2015 May 31 -June 4 Simulation Phantom Reconstructions Varying Blur Distribution 2 2 2 FWHM푇표푡푎푙 = FWHM푠 + FWHM푑 = Constant Assess effects of varying different types of blur when total blur is constant The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 5 Steven Tilley ([email protected]) Fully 3D Recon 2015 May 31 -June 4 Varying Total Blur FWHM 푠 = Constant FWHM푑 Assess effects of varying total blur when the ratio of blur widths is constant Test Bench Studies Volume: 210x600x600 Voxels: 150 µm 720 Projections Full orbit SDD: 1180 mm SAD: 600 mm Pixels: 388x388 µm 100 kVp 0.63 mAs per projection The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 6 Steven Tilley ([email protected]) Fully 3D Recon 2015 May 31 -June 4 Detector MTF Measurements E. Samei, M. J. Flynn, and D. a. Reimann, “A method for measuring the presampled MTF of digital radiographic systems using an edge test device,” Med. Phys., vol. 25, no. 1, p. 102, 1998. Source MTF The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 7 Steven Tilley ([email protected]) Fully 3D Recon 2015 May 31 -June 4 Bench Data Reconstruction Bench Data Reconstruction Difference from high resolution reference The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 8 Steven Tilley ([email protected]) Fully 3D Recon 2015 May 31 -June 4 Conclusion - More accurate noise models improve model based algorithms. - Modeling noise correlations are important in the presence of large source blurs. - Clinical systems with specs similar to our test bench will be able to better resolve fine structure such as trabeculae using this method Future directions - Model higher order characteristics of source blur - Nonlinear objective function Source Pinhole image The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 9.
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