Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Fully 3D Conference 2015 Reconstruction of Difference using Prior Images and a Penalized-Likelihood Framework Amir Pourmorteza, Hao Dang, Jeffrey Siewerdsen, J. Webster Stayman Department of Biomedical Engineering, Johns Hopkins University 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 Clinical Partners Students Industry Partners Tharindu De Silva Junghoon Lee Qian Cao Lyn Hibbard Grace Gang John Wong Hao Dang Xiao Han Aswin Mathews Sarah Ouadah Markus Eriksson Amir Pourmorteza Sureerat Reaungamornrat Himu Shukla Jeffrey Siewerdsen Steven Tilley II Alejandro Sisniega Ali Uneri J. Webster Stayman Jennifer Xu Shiyu Xu Thomas Yi Wojciech Zbijewski Funding This work was support, in part, by an academic-industry partnership grant from Elekta. The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 1 Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Sequential Imaging: IGRT Planning MDCT Subsequent Cone-Beam CTs . High-fidelity data Low-fidelity data High exposure Less radiation exposure per scan Sequential Imaging: IGRT Planning MDCT Subsequent Cone-Beam CTs . High-fidelity data Low-fidelity data High exposure Less radiation exposure per scan The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 2 Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Sequential Imaging: Brain Perfusion and Cardiac CT Low-fidelity High-fidelity Low exposure High exposure Video from: J. C. Rios, M. Luttrull, E. G. Stein, L. N. Tanenbaum.Time resolved - 4D CT Angiography: Applications and Protocols. ECR 2011 Sequential Imaging and Prior Knowledge • Prior-image-based reconstruction : – Prior image in regularization term • PICCS*: Prior Image Constrained Compressed Sensing • PIRPLE**: Prior Image Registration in Penalized Likelihood Estimation – Prior image in data fit term • Reconstruction of Difference (RoD) • The primary objective in some sequential imaging studies is to assess the difference in anatomy. *: Chen, Guang-Hong, Jie Tang, and Shuai Leng. "Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets." Medical physics 35.2 (2008): 660-663. **: Stayman, J. Webster, et al. "PIRPLE: a penalized-likelihood framework for incorporation of prior images in CT reconstruction." Physics in medicine and biology 58.21 (2013): 7563. The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 3 Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Difference Model for the Image Volume = + ∆ Current Anatomy Prior Anatomy Change in Anatomy 0.03 ∆ 0.025 0.02 0.015 0.01 0.005 0 Difference Model for the Image Volume = W + ∆ Current Anatomy Prior Anatomy Change in Anatomy 0.03 ∆ 0.025 0.02 0.015 0.01 0.005 0 The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 4 Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Image Reconstruction using Prior Images PIRPLE • Integrates prior image through a penalty term. {̂, } = argmin − ; + ∥Ψ∥1 + ∥Ψ − ∥1 ∈ℝ Data Fit Term Roughness Prior Image Registration Penalty term Penalty Term Reconstruction of Difference (RoD) • Integrates prior image/projections through the forward model. {̂∆, } = argmin − ∆, ; , + ∥Ψ∆∥1 + ∥∆∥1 ∆∈ℝ Data Fit Term Roughness Prior Magnitude Penalty term Penalty Term Image Reconstruction using Prior Images PIRPLE • Integrates prior image through a penalty term. {̂, } = argmin − ; + ∥Ψ∥1 + ∥Ψ − ∥1 ∈ℝ Data Fit Term Roughness Prior Image Registration Penalty term Penalty Term Reconstruction of Difference (RoD) • Integrates prior image/projections through the forward model. {̂∆, } = argmin − ∆, ; , + ∥Ψ∆∥1 + ∥∆∥1 ∆∈ℝ Data Fit Term Roughness Prior Magnitude Penalty term Penalty Term The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 5 Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Objective Function Optimization Forward Model: = − = W + ∆ = −∆ −W Registration update Image update = ℎ(∆) . −W = . −∆ = arg min Φ ; , , = arg min Φ ∆; , , ∈ℝ ∆∈ℝ ** find using 3D-2D find ∆ using OS-SPS registration, and BFGS * Φ(∆, ; , ) = − ∆, ; , + ∥Ψ∆∥1 + ∥∆∥1 *: Stayman, J. Webster, et al. "Model-based tomographic reconstruction of objects containing known components." Medical Imaging, IEEE Transactions on 31.10 (2012): 1837-1848. **: Erdogan, Hakan, and Jeffrey A. Fessler. "Ordered subsets algorithms for transmission tomography." PMB, 44.11 (1999): 2835. Objective Function Optimization Forward Model: = − = W + ∆ = −∆ −W Registration update Image update = ℎ(∆) . −W = . −∆ = arg min Φ ; , , = arg min Φ ∆; , , ∈ℝ ∆∈ℝ ** find using 3D-2D find ∆ using OS-SPS registration, and BFGS * Φ(∆, ; , ) = − ∆, ; , + ∥Ψ∆∥1 + ∥∆∥1 *: Stayman, J. Webster, et al. "Model-based tomographic reconstruction of objects containing known components." Medical Imaging, IEEE Transactions on 31.10 (2012): 1837-1848. **: Erdogan, Hakan, and Jeffrey A. Fessler. "Ordered subsets algorithms for transmission tomography." PMB, 44.11 (1999): 2835. The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 6 Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Objective Function Optimization Forward Model: = − = W + ∆ = −∆ −W Registration update Image update = ℎ(∆) . −W = . −∆ = arg min Φ ; , , = arg min Φ ∆; , , ∈ℝ ∆∈ℝ ** find using 3D-2D find ∆ using OS-SPS registration, and BFGS * Φ(∆, ; , ) = − ∆, ; , + ∥Ψ∆∥1 + ∥∆∥1 *: Stayman, J. Webster, et al. "Model-based tomographic reconstruction of objects containing known components." Medical Imaging, IEEE Transactions on 31.10 (2012): 1837-1848. **: Erdogan, Hakan, and Jeffrey A. Fessler. "Ordered subsets algorithms for transmission tomography." PMB, 44.11 (1999): 2835. Digital Phantom • Digital Phantom: Derived from high-fidelity CBCT data • New measurements made from: Prior + tumor • spherical tumor – 10.5 mm diameter – Attenuation 0.020 mm-1 • C-Arm Geometry: SAD = 77.5, SDD = 118.3 cm, 720 projections over 360° • Poisson measurement noise: b = 102 : 101/2 : 105 (photons) + = Prior Tumor New measurements The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 7 Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Penalty coefficient optimization ReconstructedI =10000 # projections:180 Difference I =10000 RMSE # projections:180 0 0 -3 x 10 0.02 4.5 4.5 2.5 4 0.015 4 Magnitude ∥ ∥ 3.5 3.5 2 ∆ 1 0.01 3 3 ) ) M M 1.5 ( ( 2.5 0.005 2.5 10 10 log log 2 2 0 1 1.5 1.5 * 1 -0.005 1 0.5 0.5 0.5 -0.01 0.5 1 1.5 2 2.5 0.5 1 1.5 2 2.5 log ( ) log ( ) 10 R Roughness ∥Ψ∆∥1 10 R Local vs. Global Acquisition/Reconstruction • If difference is spatially limited – ∆ is negligible outside VOI • Local Reconstruction – Usually not possible in Model-Based Reconstruction – Computational speedup ∆ • Local (truncated) Acquisition – Radiation dose reduction 1 = −W −∆ The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 8 Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Global vs. Local Acquisition Global RoD Local RoD 0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 -3 x 10 ̂∆ + 12 10 8 6 4 2 Fluence = 104 (photons) ̂∆ 0 180 projections RMSE: 4.19 4.02 ×10-4 mm-1 Performance: Sparse Acquisitions -3 x 10 5 PL RoD 4 ) 1 - 3 2 RMSE RMSE (mm 1 Fluence= 104 (photons) 0 0 100 200 300 400 # of projections PL 0.045 0.04 ̂ 0.035 0.03 0.025 RoD 0.02 0.015 ̂∆ + 0.01 0.005 16 24 45 90 180 360 The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 9 Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Performance: Sparse Acquisitions -3 x 10 5 PL RoD 4 ) 1 - 3 2 RMSE RMSE (mm 1 Fluence= 104 (photons) 0 0 100 200 300 400 # of projections 0.03 PL 0.045 0.04 0.02 0.035 ̂ − 0.010.03 0.025 RoD 0 0.02 -0.010.015 ̂∆ 0.01 -0.02 0.005 16 24 45 90 180 360 Performance: Varying Fluence -3 6 x 10 PL 5 RoD ) 1 - 4 (mm 3 2 RMSE 1 # of projections: 90 0 2 3 4 5 10 10 10 10 Incident Fluence 0.03 PL 0.045 0.020.04 0.035 0.01 0.03 00.025 RoD 0.02 -0.01 0.015 + ∆ -0.020.01 0.005 -0.03 102 105 (photons) The I-STAR Laboratory (istar.jhu.edu) and The AIAI Laboratory (aiai.jhu.edu) Department of Biomedical Engineering Johns Hopkins University 10 Amir Pourmorteza Fully 3D Recon 2015 [email protected] May 31 -June 4 Performance: Varying Fluence -3 6 x 10 PL 5 RoD ) 1 - 4 3 2 RMSE RMSE (mm 1 # of projections: 90 0 2 3 4 5 10 10 10 10 Incident Fluence 0.03 PL 0.02 − 0.01 0 RoD -0.01 ∆ -0.02 -0.03 102 105 (photons) Performance of Likelihood-based Registration • Prior image transformed by a known rigid transform.