1. J. A. O ’ Sullivan, Quantitative Imaging, 11/19/12 P-20 Seminar, 3/12/05 R. M. Arthur Quantitative Imaging: X-Ray CT and Transmission Tomography Joseph A. O ’ Sullivan Samuel C. Sachs Professor Dean, UMSL/WU Joint Undergraduate Engineering Program Professor of Electrical and Systems Engineering, Biomedical Engineering, and Radiology jao@wustl.edu Supported by Washington University and NIH-NCI grant R01CA75371 (J. F. Williamson, VCU, PI).

2. J. A. O ’ Sullivan, Quantitative Imaging, 11/19/12 P-20 Seminar, 3/12/05 R. M. Arthur Collaborators Norbert Agbeko Yaqi Chen Liangjun Xie Daniel Keesing Daheng Li Josh Evans, VCU Ikenna Odinaka Debashish Pal Jasenka Benac Giovanni Lasio, VCU Bruce R. Whiting David G. Politte Jeffrey F. Williamson, VCU Donald L. Snyder David Brady, Duke Richard Laforest Yuan-Chuan Tai FacultyStudents Chemical Engineers M. Dudukovic M. Al-Dahhan R. Varma

3. J. A. O ’ Sullivan, Quantitative Imaging, 11/19/12 P-20 Seminar, 3/12/05 R. M. Arthur Dual Energy CT Image Reconstruction Scanners Data Models  Reconstruction Algorithms Image Reconstruction Approaches –“Linear” Approaches –Statistical Iterative Reconstruction Experiment SOMATOM Definition CT Scanner ccir.wustl.edu

4. J. A. O ’ Sullivan, Quantitative Imaging, 11/19/12 P-20 Seminar, 3/12/05 R. M. Arthur X-Ray CT Scanners Manufacturers: Siemens, GE, Philips, Toshiba, Analogic “Third Generation” vs. flat panel Rotate 3 times per second Detectors sampled approximately 1000 times per rotation 16 – 64 rows of detectors 600+ detectors per row Siemens has two heads > 5.4E7 samples per second Reconstructed volumes 512 by 512 by 200 SOMATOM Definition CT Scanner ccir.wustl.edu

5. J. A. O ’ Sullivan, Quantitative Imaging, 11/19/12 P-20 Seminar, 3/12/05 R. M. Arthur X-Ray Transmission Tomography— Basics Source Spectrum, Energy E Beer’s Law and Attenuation Mean Photons/Detector I 0 Beam-hardening Detector Sensitivity Spectrum Mean (Photon) Flux J. L. Prince and J. Links, Medical Imaging Signals and Systems. Pearson Education: Upper Saddle River, NJ, 2006.

6. J. A. O ’ Sullivan, Quantitative Imaging, 11/19/12 P-20 Seminar, 3/12/05 R. M. Arthur Beer’s Law Attenuation includes absorption and scatter Attenuation is related to survival probabilities –The probability that a photon survives going through n chunks of material is the product of the probabilities of surviving individual chunks –The limit of the product of many terms is the exponential of an integral –The integral is through the attenuation function

7. J. A. O ’ Sullivan, Quantitative Imaging, 11/19/12 P-20 Seminar, 3/12/05 R. M. Arthur “Linear” Image Reconstruction Normalize relative to an air scan Beam-hardening correction to target energy Negative log to estimate line integrals at target energy Linear inversion, normalize (e.g. water-equivalent) Normalize & correct FBP normalize Negative logarithm

8. J. A. O ’ Sullivan, Quantitative Imaging, 11/19/12 P-20 Seminar, 3/12/05 R. M. Arthur Limitations and Implementation Real detectors measure random data –Electronics noise, quantization, photon-counting noise Linearized model: –Measure all line-integrals (Radon transform) –Invert this linear mapping (Inverse Radon transform or filtered back-projection (FBP)) Today: –Measure flux through beakers with copper sulfate –Estimate attenuation relative to no copper sulfate –Approximate as a linear mapping –Invert this linear mapping

9. J. A. O ’ Sullivan, Quantitative Imaging, 11/19/12 P-20 Seminar, 3/12/05 R. M. Arthur Inversion of Linear Mappings 1.Approximate: Find some reasonable estimate that give predicted data close to the measurements. 2.Ideally: Given linear measurements, find the estimate that minimizes the sum of the square errors between the measurements and the predicted measurements.