Noise, Detectability, and Implications for System Design
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Task-Based Imaging Performance in 3D X-Ray Tomography: Noise, Detectability, and Implications for System Design by Jianan (Grace) Gang A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Institute of Biomaterials and Biomedical Engineering University of Toronto © Copyright by Jianan (Grace) Gang 2014 Task-Based Imaging Performance in 3D X-Ray Tomography: Noise, Detectability, and Implications for System Design Jianan (Grace) Gang Doctor of Philosophy Institute of Biomaterials and Biomedical Engineering University of Toronto 2014 Abstract Quantifying imaging performance is an important aspect in the development, optimization, and assessment of medical imaging systems. This thesis addresses new challenges in the characterization of imaging performance for advanced x-ray tomographic imaging technologies. Central to the work is a task-based cascaded systems analysis framework that encompasses aspects of system geometry, x-ray beam characteristics, dose, detector design, background anatomy, model observers, and the imaging task. The metrology throughout includes Fourier domain descriptors of spatial resolution (modulation transfer function, MTF), noise (noise-power spectrum, NPS), noise-equivalent quanta (NEQ), and task-based detectability. Central elements and advances of the work include: a task-based model for 3D imaging performance in tomosynthesis and cone-beam CT (CBCT); generalization of imaging performance metrics to include the influence of anatomical background clutter; validation of the model in comparison to human observer performance; extension to dual-energy (DE) tomographic imaging; analysis of non-stationary (i.e., spatially varying) signal and noise characteristics; and extension to model- based statistical image reconstruction. In each case, the analytical framework demonstrates the ii importance of task-based assessment and the capability for system optimization in a fairly broad scope of clinical applications ranging from breast to abdominal and musculoskeletal imaging. The validity of the framework in describing “local” signal and noise characteristics is demonstrated under conditions of strong nonstationarity, ranging from simple phantoms to complex anthropomorphic scenes. In addition to providing a framework for system design and optimization, the analysis opens potential new opportunities in task-based imaging and statistical reconstruction, with examples demonstrated in the design of optimal regularization in iterative reconstruction. iii Acknowledgments First and foremost, I would like to thank my supervisor, Dr. Jeff Siewerdsen. He introduced me to the exciting world of medical physics when I was just a clueless summer student and fostered my interest in science and engineering into a potential career. He had not only offered his invaluable expertise in medical imaging, but provided me with tremendous support and encouragement. This work would not be possible without his guidance. His unwavering passion for science will always be an inspiration to me. I would also like to thank the members of my supervisory committee, Drs. Krsity Brock and Mike Joy, for their support and helpful comments. Members of my exam committee, Drs. David Jaffray, Martin Yaffe, and John Boone are gratefully acknowledged. I am deeply grateful for the collaboration and support from my colleagues who helped to make this work possible - chronologically, Dr. Samuel Richard for teaching me what NPS, MTF, and IPA are; Daniel Tward for sharing with me his insights in image science and many interesting math puzzles; Dr. Junghoon Lee for remotely working with me on the observer study which materialized into Chapter 4 of this thesis; Dr. Wojtek Zbijewski for his valuable assistance with the dual-energy study in Chapter 5; and last but not least, Dr. Web Stayman for his mentorship in the last leg of my studies and for sharing with me his expertise in statistical reconstruction. I am lucky to have worked in two great labs – the IGTx lab at the University of Toronto and the ISTAR lab at Johns Hopkins University. Staff and students in both labs have made my journey through graduate school an enjoyable one: Hany, Carlos, Thao, Nate, Angela, Mike, Harley, Jenny, Carolyn, Jordan, Steve, Greg, Nick, Sun-mo, and Noor from Toronto; Ja, Adam, Ali, Yoshi, Sebastian, Saj, Muhit, Yifu, Paul, Dan, Prakhar, Hao, Jen and Zhe from Hopkins. I am forever grateful to my dearest friends, old and new, for being part of my life: Tina, Neil, and Sheryl, for always being there for me and willing to lend an ear/shoulder; Chunjing, Zhong, Zhu, Siyu, and Christine, for friendship through the years and hopefully for many more to come; the EngSci crew, especially Yinming, John, Luke, and Chunpo, for all the fun and games and making Toronto feel like home; Huihui, for the ever-so-effective shopping therapy; Yuxuan, Carmen, and Claire, for inspiring me with their dedication towards work and good food, and for making life in Baltimore fun and exciting. iv Last but not least, I would like to thank my family, especially my parents, to whom I am infinitely indebted. Words cannot express my gratitude for their love and kindness, for allowing me to pursue my dreams in a faraway land, and for supporting me to be an educated, independent woman. Thank you! v Table of Contents ACKNOWLEDGMENTS ......................................................................................................................... IV TABLE OF CONTENTS .......................................................................................................................... VI LIST OF TABLES ................................................................................................................................... XII LIST OF FIGURES ................................................................................................................................ XIII LIST OF APPENDICES .......................................................................................................................XVII LIST OF NOTATIONS ...................................................................................................................... XVIII CHAPTER 1 ............................................................................................................................................... 1 INTRODUCTION...................................................................................................................................... 1 CHAPTER 2 ............................................................................................................................................... 5 THEORETICAL BACKGROUND ........................................................................................................... 5 2.1. FOURIER DOMAIN IMAGING PERFORMANCE METRICS ................................................... 5 2.1.1. Linear and Shift-Invariant (LSI) Systems ....................................................................................................... 5 2.1.2. Stationarity .................................................................................................................................................. 6 2.1.3. Modulation Transfer Function (MTF) ........................................................................................................... 7 2.1.4. Noise-Power Spectrum (NPS) ..................................................................................................................... 10 2.1.5. Detective Quantum Efficiency (DQE) and Noise Equivalent Quanta (NEQ) ................................................. 12 2.2. CASCADED SYSTEM ANALYSIS ................................................................................................ 14 2.2.1. Signal and Noise Transfer Characteristics ................................................................................................... 14 2.2.1.1. Gain Stages ................................................................................................................................................. 15 2.2.1.2. Deterministic Spreading Stage ................................................................................................................... 16 2.2.1.3. Stochastic Spreading Stage ........................................................................................................................ 17 vi 2.2.1.4. Sampling Stage ........................................................................................................................................... 18 2.2.2. Cascaded Systems Analysis ........................................................................................................................ 19 2.2.2.1. Stage 0: Incident quanta ............................................................................................................................ 21 2.2.2.2. Stage 1: Quantum Detection Efficiency...................................................................................................... 22 2.2.2.3. Stage 2: Conversion from X-Rays to Optical Photons ................................................................................. 23 2.2.2.4. Stage 3: Spreading of Secondary Quanta in the X-Ray Converter .............................................................. 29 2.2.2.5. Stage 4: Coupling of Secondary Quanta to Detector Apertures................................................................. 31 2.2.2.6. Stage 5: Integration of secondary quanta by detector pixel aperture ......................................................