3D Filtered Backprojection Fundamentals, Practicalities, and Applications

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. H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: jeff.siewerdsen@jhu.

Hopkins University Schools of Medicine and Engineering Acknowledgments I-STAR Laboratory Imaging for Surgery, Therapy, and Radiology www.jhu.

1 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Education Image Reconstruction I 3D Filtered Backprojection Fundamentals, Practicalities, and Applications eff Siewerdsen, PhD Department of Biomedical Engineering ohns Hopkins University ohns Hopkins University Schools of Medicine and Engineering Acknowledgments I-STAR Laboratory Imaging for Surgery, Therapy, and Radiology Hopkins Collaborators W Stayman, W Zbijewski (BME) Y Otake, Lee (Comp. Science) R Taylor, G Hager (Comp. Science) Prince (Electrical Engineering) D Reh (Head and Neck Surgery) G Gallia (Neurosurgery) Khanna (Spine Surgery) Wong (Radiation Oncology) Carrino (MSK Radiology) Funding Support National Institutes of Health Carestream Health (Rochester NY) Siemens Healthcare (XP, Erlangen) Disclosures Medical Advisory Board, Carestream Health Medical Advisory Board, Siemens Healthcare Elekta Oncology Systems Department of Biomedical Engineering ohns Hopkins University 1

2 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Evolution and Proliferation of CT Sir Godfrey Hounsfield Nobel Prize, 1979 Evolution and Proliferation of CT c c Department of Biomedical Engineering ohns Hopkins University 2

Image Quality Artfiacts Spatial Resolution Contrast Resolution Noise Proliferation and Applications Diagnostic imaging Image-guided interventions First-Generation CT Scan and

3 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Overview Computed Tomography Generations Natural history and new technology 3D Image Reconstruction Filtered backprojection Basics and practicalities Open-source resources Image Quality Artfiacts Spatial Resolution Contrast Resolution Noise Proliferation and Applications Diagnostic imaging Image-guided interventions First-Generation CT Scan and Rotate: Linear scan of source and detector Line integral measured at each position: p(x) x x x x x x x x Rotate source-detector Dq Repeat linear scan Projection data: p(x,q) p(x) Department of Biomedical Engineering ohns Hopkins University 3

Pencil Beam Translation / Rotation Fan Beam Translation / Rotation WA

rd Generation (1976) 4 th Generation (1978) Fan Beam Continuous

4 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: CT Generations 1 st Generation (1970) 2 nd Generation (1972) Pencil Beam Translation / Rotation Fan Beam Translation / Rotation WA Kalender, Computed Tomography, 2 nd Edition (2005) CT Generations 3 rd Generation (1976) 4 th Generation (1978) Fan Beam Continuous Rotation WA Kalender, Computed Tomography, 2 nd Edition (2005) Fan Beam Continuous Tube Rotation Stationary Detector Department of Biomedical Engineering ohns Hopkins University 4

edu Helical (Spiral CT) Pitch <1 : Overlap Higher z-resolution Higher dose

increment / rotation (mm) Beam collimation width (mm) WA Kalender, Computed

complete x-ray and data acquisition systems on one gantry.

5 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Helical (Spiral CT) Pitch <1 : Overlap Higher z-resolution Higher dose Pitch >1: Non-overlap Lower z-resolution Lower patient dose Pitch = Table increment / rotation (mm) Beam collimation width (mm) WA Kalender, Computed Tomography, 2 nd Edition (2005) Dual-Source CT University of Zurich zoom Two complete x-ray and data acquisition systems on one gantry. 330 ms rotation time (effective 83 ms scan time) Siemens Healthcare Somatom Definition Department of Biomedical Engineering ohns Hopkins University 5

Reconstruction Multiple Rotations Cone-Beam CT: Cone-Beam Collimation Large-Area Detector 3-D Volume Images

6 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Recent Advances: Cone-Beam CT Fully 3-D Volumetric CT Conventional CT: Fan-Beam 1-D Detector Rows Slice Reconstruction Multiple Rotations Cone-Beam CT: Cone-Beam Collimation Large-Area Detector 3-D Volume Images Single Rotation Filtered Backprojection: The Basics Department of Biomedical Engineering ohns Hopkins University 6

7 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Implementation Loop over all views (all q) Projection at angle q p(x,q) Filtered Projection g(x,q) Backproject g(x,q). Add to image m(x,y) m(x,y) The Sinogram p(x,q) p(x) The Sinogram: Line integral projection p(x) measured at each angle q p(x;q) Sinogram q p(x;q) x Department of Biomedical Engineering ohns Hopkins University 7

8 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Filtered Backprojection Simple Backprojection: Trace projection data p(x;q) through the reconstruction matrix from the detector (x) to the source Simple backprojection yields radial density (1/r) Therefore, a point-object is reconstructed as (1/r) Solution: Filter the projection data by a ramp filter r p(x;q) X-ray source Filtered Backprojection The Filtered Sinogram: Convolve with RampKernel(x) p(x)*rampkernel(x) Equivalent to Fourier product M(f x ) f x p(x;q) p(x;q) q p(x;q)*rampkernel(x) x X-ray source Department of Biomedical Engineering ohns Hopkins University 8

. H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: jeff.

edu Filtered Backprojection Projection Data p(x,q) 3D Reconstruction (Axial

9 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Filtered Backprojection Projection Data p(x,q) 3D Reconstruction (Axial Slice) m(x,y,z) Cone-Beam Geometry Definitions and Coordinate Systems Department of Biomedical Engineering ohns Hopkins University 9

edu 3D Filtered Backprojection Raw Projection Data 3D Filtered

10 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: 3D Filtered Backprojection Raw Projection Data 3D Filtered Backprojection Offset-Gain (and Defect) Correction Department of Biomedical Engineering ohns Hopkins University 10

3D Filtered Backprojection Cosine Weighting

11 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: 3D Filtered Backprojection Log Normalization 3D Filtered Backprojection Cosine Weighting (Feldkamp Weights) v u Department of Biomedical Engineering ohns Hopkins University 11

edu 3D Filtered Backprojection Data Redundancy (Parker) Weights q u 3D

12 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: 3D Filtered Backprojection Data Redundancy (Parker) Weights q u 3D Filtered Backprojection Ramp Filter Department of Biomedical Engineering ohns Hopkins University 12

13 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: 3D Filtered Backprojection Smoothing / Apodization Filter Evolution of the Projection Data Department of Biomedical Engineering ohns Hopkins University 13

edu 3D Filtered Backprojection Backprojection Repeat # of voxels # of

14 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: 3D Filtered Backprojection Backprojection Repeat # of voxels # of projections Evolution of the 3D Recon Department of Biomedical Engineering ohns Hopkins University 14

edu/istar/downloads MATLAB Source code (m) Function call (m) Executable UI (exe) Intended user Education Research Input

Flexible, transparent Filters, voxel size, Reconstruction filters Open-Source Resources PortoRECO Portable Reconstruction

15 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Open-Source Resources OSCaR Open-Source Cone-Beam Reconstructor MATLAB Source code (m) Function call (m) Executable UI (exe) Intended user Education Research Input data types jpg, raw, png, etc. Flexible, transparent Filters, voxel size, Reconstruction filters Open-Source Resources PortoRECO Portable Reconstruction C# / C++ Source code (C#) Executable UI (exe) Intended user Education Research Input data types jpg, raw, png, etc. Flexible, transparent Filters, voxel size, Reconstruction filters Department of Biomedical Engineering ohns Hopkins University 15

16 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Artifacts Artifacts Rings Shading Streaks Motion Lag Metal Truncation Cone-Beam Department of Biomedical Engineering ohns Hopkins University 16

17 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: 1) Reduced contrast Reduction of DCT# 2) Image artifacts Cupping and streaks Artifacts: X-ray Scatter Contrast (mm -1 ) BR-SR1 Breast in Water 3) Increased image noise Reduced DQE C SPR 0 d e Reduced soft-tissue detectability C' C o ln d 1 SPR SPR (%) A big problem for cone-beam CT: SPR is very large for large cone angles (i.e., large FOV) Artifacts: X-ray Scatter 1) Reduced contrast Reduction of DCT# 2) Image artifacts Cupping and streaks 3) Increased image noise Reduced DQE Reduced soft-tissue detectability A big problem for cone-beam CT: SPR is very large for large cone angles (i.e., large FOV) Department of Biomedical Engineering ohns Hopkins University 17

18 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Artifacts: X-ray Scatter 1) Reduced contrast Reduction of DCT# 2) Image artifacts Cupping and streaks 3) Increased image noise Reduced DQE Reduced soft-tissue detectability SPR (%) 100 Pelvis Abdomen 10 Chest Extremity Air Field of View (z) (cm) A big problem for cone-beam CT: SPR is very large for large cone angles (i.e., large FOV) Image Quality Key Image Quality Metrics Image Uniformity CT # Accuracy Spatial resolution Contrast resolution Noise (and NPS) CNR NEQ Department of Biomedical Engineering ohns Hopkins University 18

statistics Physical effects: Quantum noise Bowtie filter Sampling effects: Intrinsic to FBP Number of projections View aliasing (3.8 ± 4.2) (5.6 ± 2.4) (-1.3 ± 6.2) (4.4 ± 4.

00-10 0 +10 Distance (mm) Uniformity / Stationarity Signal Uniformity Stationarity of the mean Shading artifacts Beam-hardening Truncation Variance Maps s 2 (x,y) s 2 (/mm)2 Noise

19 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Uniformity / Stationarity Signal Uniformity Stationarity of the mean Shading artifacts Beam-hardening Truncation Noise Uniformity Stationarity of the noise WSS of second-order statistics Physical effects: Quantum noise Bowtie filter Sampling effects: Intrinsic to FBP Number of projections View aliasing (3.8 ± 4.2) (5.6 ± 2.4) (-1.3 ± 6.2) (4.4 ± 4.2) Mean Signal (/mm) (4.6 ± 3.2) 0.20 D HU = ( ) HU = 3.3 HU SPR ~0 SPR ~100% Distance (mm) Uniformity / Stationarity Signal Uniformity Stationarity of the mean Shading artifacts Beam-hardening Truncation Variance Maps s 2 (x,y) s 2 (/mm)2 Noise Uniformity Stationarity of the noise WSS of second-order statistics Physical effects: Quantum noise Bowtie filter Sampling effects: Intrinsic to FBP Number of projections View aliasing Variance Cylinder + Bowtie Cylinder + Bowtie Air Water Cylinder Air Distance (mm) Water Cylinder Department of Biomedical Engineering ohns Hopkins University 19

edu Spatial Resolution (line-pairs per mm) Minimum resolvable line-pair

20 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Spatial Resolution (line-pairs per mm) Minimum resolvable line-pair group Spatial Resolution (Modulation Transfer Function) Department of Biomedical Engineering ohns Hopkins University 20

Signal (mm -1 ) 127 mm Wire in H 2 O 1.0 0.8 0.6 0.4 0.2 0.

0 Spatial Frequency (mm -1 ) MTF f, f FT LSF x, y x y

efficiency Voxel size Axial, a xy Slice thickness, a z

21 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Spatial Resolution (Modulation Transfer Function) Signal (mm -1 ) 127 mm Wire in H 2 O Measured Steel Wire System MTF Spatial Frequency (mm -1 ) MTF f, f FT LSF x, y x y Image Noise CT image noise depends on Dose Detector efficiency Voxel size Axial, a xy Slice thickness, a z Reconstruction filter 2 s k K E 1 D a o xy 3 xy az Barrett, Gordon, and Hershel (1976) Department of Biomedical Engineering ohns Hopkins University 21

. H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: jeff.siewerdsen@jhu.edu Image Noise Dose Reconstruction Filter Noise (CT#) 60 50 40 30 20 10 s ~ a b X Smooth Sharp 0 0 0.5 1.

22 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Image Noise Dose Reconstruction Filter Noise (CT#) s ~ a b X Smooth Sharp Dose (mgy) Noise-Power Spectrum The NPS describes Frequency content (correlation) NPS a ax y az f, f, f DFT DI x, y, z x y L L Magnitude of fluctuations z x y L z 2 Department of Biomedical Engineering ohns Hopkins University 22

23 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Noise-Power Spectrum Axial Plane (x,y) Axial NPS S(f x, f y ) Noise-Power Spectrum Sagittal Plane (x,z) Sagittal NPS S(f x, f z ) Department of Biomedical Engineering ohns Hopkins University 23

domain: Band-limited Low-Pass Contrast A large-area transfer characteristic Defined: As an absolute

02 cm -2 or C = -100 HU 0 HU = 100 HU ROI #2 ROI #1 As a relative difference in mean pixel values:

24 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: NPS(f x, f y, f z ) Noise-Power Spectrum Axial domain: Filtered-ramp Mid-Pass Longitudinal domain: Band-limited Low-Pass Contrast A large-area transfer characteristic Defined: As an absolute difference in mean pixel values: For example: C = 0.18 cm cm -1 = 0.02 cm -2 or C = -100 HU 0 HU = 100 HU ROI #2 ROI #1 As a relative difference in mean pixel values: For example: C = 0.18 cm cm cm -1 ~ 10% Department of Biomedical Engineering ohns Hopkins University 24

25 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Contrast-to-Noise Ratio CNR Soft-Tissue-Simulating Spheres 100 kvp 103 HU 88 HU 66 HU 45 HU 25 HU 22 HU 11 HU Dose to Isocenter (mgy) 23.3 mgy 9.6 mgy 2.9 mgy 0.6 mgy Proliferation of CT Technologies and Applications Diagnostic Imaging Specialty Applications and Image-Guided Procedures Trade names removed. Department of Biomedical Engineering ohns Hopkins University 25

26 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Proliferation of CT Technologies and Applications Breast Screening / Diagnosis. M. Boone (UC Davis) Iodine-Enhanced Tumor Imaging Proliferation of CT Technologies and Applications Upper Extremities Morphology, Function, and Quantitation Dual-Energy CBCT Lower Extremities Weight-Bearing Iodine Calcium Department of Biomedical Engineering ohns Hopkins University 26

27 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Proliferation of CT Technologies and Applications Skull Base Surgery CBCT C-Arm Spine / Orthopaedics Thoracic Surgery Proliferation of CT Technologies and Applications Head and Neck Sarcoma Lung Prostate Department of Biomedical Engineering ohns Hopkins University 27

28 . H. Siewerdsen et al. (AAPM 2011, Vancouver BC) For PPT slides, contact: Summary and Conclusions Proliferation of CT Increased utilization (and related challenges) New technology (e.g., cone-beam CT) Specialty applications Open Source OSCaR, PortoRECO Others? (Please contact me.) More to Come This Week: 1.) Siewerdsen Filtered Backprojection Fundamentals (MON-A-311) 2.) Fessler Iterative Image Reconstruction (TUE-A-211) 3.) Yu Optimization of image acquisition and recon (WED-E-110) Information and Handouts: Department of Biomedical Engineering ohns Hopkins University 28

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