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

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 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 1 Steven Tilley ([email protected]) Fully 3D Recon 2015 May 31 -June 4

Noise model and reality mismatch

NormalizedDetectorUnits NormalizedDetectorUnits

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