The Generalized NEQ and Detectability Inde for Tomosynthesis and Cone-Beam CT Grace J. Gang 1, Junghoon Lee 2, J. Webster Stayman 3, Daniel Tward 3,W. Zbijewski 3, Jerry L. Prince 2, and Jeffrey H. Siewerdsen 1,3 1 Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto ON 2 Electrical and Computer Engineering, Johns Hopkins University, Baltimore MD 3 Dept. of Biomedical Engineering, Johns Hopkins University, Baltimore MD Biomaterials and Biomedical Engineering University of Toronto Biomedical Engineering Johns Hopkins University
Consortium Johns Hopkins University University of Toronto Jeff Siewerdsen Jerry Prince Web Stayman Junghoon Lee Wojtek Zbijewski Daniel Tward Grace Gang Stanford University Rebecca Fahrig Sungwon Yoon CSU Fullerton Angel Pineda Harvard Medical School Art Burgess (ret.) Acknowledgments
Motivation 2A Cascaded Systems Analysis (CSA) Etension of Fourier performance metrics (NEQ) to advanced imaging applications NEQ Task Detectability Inde (d ) General quantitative metrics for performance assessment incorporating imaging tasks 0 1 2B 3 4 5 6 7 2C 13 12 11 W task (f) 10 9 System Performance and Optimization Investigate the etent to which d is a valid metric for performance evaluation Correspondence with real observers A z Theory Measurement θ tot
Bridging the Gap Fourier Metrics (GNEQ) Fundamental Image Science Real Observer Response 2A 0 1 2B 3 4 5 6 7 2C 13 12 11 10 9 Generalized Detectability Theory A z Measurement θ tot
Cascaded Systems Analysis Projection Formation Reconstruction by Filtered Backprojection Generalized Detectability Inde d = ' 2 3D 2 T [ T W ] S B Task T System MTF S Q Quantum NPS W Task Imaging task S E Electronics NPS Q 2 + S + S E df df df y z S B = κ f β S B - Anatomical background power spectrum (Power-law)
Model Observers (d ) Prewhitening observer (PW)
Model Observers (d ) Prewhitening observer (PW) PW observer with eye filter and internal noise (PWEi)
Model Observers (d ) Prewhitening observer (PW) PW observer with eye filter and internal noise (PWEi) Non-prewhitening observer (NPW)
Model Observers (d ) Prewhitening observer (PW) PW observer with eye filter and internal noise (PWEi) Non-prewhitening observer (NPW) NPW observer with eye filter (NPWE)
Model Observers (d ) Prewhitening observer (PW) PW observer with eye filter and internal noise (PWEi) Non-prewhitening observer (NPW) NPW observer with eye filter (NPWE) NPWE observer with internal noise (NPWEi)
Model Observers (d ) Prewhitening observer (PW) PW observer with eye filter and internal noise (PWEi) Non-prewhitening observer (NPW) NPW observer with eye filter (NPWE) NPWE observer with internal noise (NPWEi) Slice Detectability Inde - Integrate over direction orthogonal to slice d [ T W df ] 2 ' 2 Task y slice = df 2 dfz T SB + SQ + SEdf y
Eperimental Conditions A Clutter Phantom for Power-Law Noise Design principle: self-similarity S B Equal volumes of differently-sized spheres κ β 3 radiograph = f β β (θ tot ) tomosynthesis and CBCT TWO Scenarios: Variable θ tot θ tot = 20 θ tot = 90 θ tot = 120 θ tot = 200 Constant θ θ = 0.45 o Variable total dose f y Constant N proj N proj = 89 Fied total dose f y f f f f
Imaging Tasks Clutter Phantom Si stimuli in the central coronal (-z) slice Uniform Background Phantom Acrylic sphere on polyurethane background Polyurethane Line drawing Acrylic Five Imaging Tasks Sphere Detection in Uniform Background Small Sphere Detection Large Sphere Detection Cube vs. Sphere Encapsulated Sphere vs. Solid Sphere
Observer Study 9 AFC Human Observer Measurements 9-Alternative Forced-Choice (AFC) Test Darkened reading room Monochrome diagnostic-quality display Fied win / level [90%*min, 110%*ma] 8 observers (physicists) Training set distinct from test set 5 trials (distinct stimuli) Randomized reading order ~100 minutes for each observer
Observer Study 9 AFC Theoretical calculation (cascaded systems + task + model observer) 1 d ' A Z = (1 +erf ( )) 2 2 P corr A Z d' 2 1 ( d) M 1 Pcorr ( d', M) = ep [ φ( ) ] d 2π 2 Measured directly from human observer MAFC tests
Theory vs. Measurement 1. Sphere Detection on Uniform Background Question to observer: Which image contains a ¼ sphere at the center W Task 10 0 A z 1.0 0.8 Constant θ PW, PWEi, NPW, NPWE NPWEi Human Observer f z B 0.6 10-8 0.4 f 0 60 120 180 240 300 360 θ tot 10 o 40 o 120 o 200 o 280 o 360 o z
Theory vs. Measurement 1. Sphere Detection on Uniform Background Question to observer: Which image contains a ¼ sphere at the center W Task 10 0 A z 1.0 0.8 Constant N proj PW, PWEi, NPW, NPWE NPWEi Human Observer f z B 0.6 10-8 0.4 f 0 60 120 180 240 300 360 θ tot 10 o 40 o 120 o 200 o 280 o 360 o z
Theory vs. Measurement 2. Small Sphere Detection on Cluttered Background Question to observer: Which image has a high contrast 1/8 sphere at the center f z W Task 10 0 10-6 B A z 1.0 0.8 0.6 0.4 PW, PWEi Constant θ NPW NPWEi Human Observer NPWE f 0 60 120 180 240 300 360 θ tot 10 o 40 o 120 o 200 o 280 o 360 o z
Theory vs. Measurement 2. Small Sphere Detection on Cluttered Background Question to observer: Which image has a high contrast 1/8 sphere at the center f z W Task 10 0 10-6 B A z 1.0 0.8 0.6 0.4 PW, PWEi Constant N proj NPW NPWEi Human Observer NPWE f 0 60 120 180 240 300 360 θ tot 10 o 40 o 120 o 200 o 280 o 360 o z
Theory vs. Measurement 5. Encapsulated Sphere vs. Solid Sphere Question to observer: Which image has a ½ diameter encapsulated sphere at the center f z W Task f 10 0 10-8 B A z 1.0 0.8 0.6 0.4 PW, PWEi Constant θ NPW NPWEi Human Observer NPWE 0 60 120 180 240 300 360 θ tot 10 o 40 o 120 o 200 o 280 o 360 o z
Theory vs. Measurement 5. Encapsulated Sphere vs. Solid Sphere Question to observer: Which image has a ½ diameter encapsulated sphere at the center f z W Task 10 0 B A z 1.0 0.8 0.6 PW, PWEi Constant N proj NPWE NPW NPWEi Human Observer f 10-8 0.4 0 60 120 180 240 300 360 θ tot 10 o 40 o 120 o 200 o 280 o 360 o z
Conclusions Detectability Inde (d ) GNEQ + Imaging Task + Observer Model(s) Shown to provide a valid metric for imaging performance and system optimization Assumptions and Limitations Stationarity (local NPS image center or fied radius) 1 Shift-invariance (task > voel size) 2 Simple, idealized imaging tasks Future Work Broader range of imaging conditions (dose) and reconstruction techniques (binning and sampling) More comple (higher order) imaging tasks 1. Pineda (SPIE 2007) 2. analogous to Albert and Maidment (Med Phys 2000)
Acknowledgements and Support The I-STAR Lab Imaging for Surgery, Therapy, and Radiology JH Siewerdsen, JW Stayman, J Lee W Zbijewski, S Schafer, Y Otake, P DeJean P Prakash, S Nithiananthan, A Uneri D Mirota, Y Ding, S Reaungamornrat, J Yoo Collaboration Jerry Prince (Johns Hopkins University) Russ Taylor (Johns Hopkins University) Rebecca Fahrig (Stanford University) Angel Pineda (CSU Fullerton) Art Burgess (Harvard University, ret.) Funding National Institutes of Health R01-CA112163 National Institutes of Health R01-CA127444