Ke Li and Guang-Hong Chen

Transcription

1 Ke Li and Guang-Hong Chen

2 Brief introduction of x-ray differential phase contrast (DPC) imaging Intrinsic noise relationship between DPC imaging and absorption imaging Task-based model observer studies for DPC imaging Summary

3 Absorption Contrast Differential Phase Contrast G1 grating G zgrating T Tomosynthesis CT ( ( xy, ) Tube G0 grating A. Momose, et al, Optical Express, 11 (303) (003) T. Weitkamp, et al, Opt. Exp. 1(16), pp , 005. F. Pfeiffer, et al, Nature Physics, pp , Apr 006. Detector 3

4 x-ray shutter active grating area Zambelli et al., Med. Phys., 010, Vol. 37, pp phase-stepping stage 4

5 detector phase grating Zambelli et al., Med. Phys., 010, Vol. 37, pp rotary stage 5

6 G 0 Absorption Grating 15 µm opening 37 µm pitch cm x cm 60 µm Au depth G 1 Phase Grating (π differential shift for 50% of beam) 4 µm opening 8 µm pitch 7 cm x 7 cm 40 µm etch depth G Absorption Grating.5 µm opening 4.5 µm pitch 7 cm x 7 cm size 30 µm Au depth All gratings were made by Joe Zambelli and Ke Li using the on-campus microfabrication facility: Wisconsin Center for Microelectronics (WCAM) at UW-Madison. 6

7 Detector Signal (arb. units) Absorption Phase I 1 I 0 I m n x I m n I m n x m n p, ; g 0, 1, cos g d, Phase Step Modulation Grating Position (m) 7

8 Absorption: Proj, dl A x y l Convolution kernel: f Ramp filter 0 f DPC: Proj DPC d p x, y l dl Convolution kernel: p sgn ( f ) d i Hilbert filter 0 f 8

9 e log I k Log. Absorption Projections Raw Detector Counts I k NPS dpc NPS ab tan Phase Retrieval I sin( / ) 1 k k K Ik cos( k / K) DPC Projections I I 1 0 G.-H. Chen et. al, Med. Phys. (010) 9

10 Without grating Log. Absorption Projections NPS dpc 1 NPS ab With grating Phase Retrieval DPC Projections 10

11 The NPS of DPC-CT can be quantitatively determined from the NPS of the associated ACT (and vice-versa) NPS DPC C g 1 f NPS ab where C g 1 p z T This relationship independent of: Dose and X-ray tube/detector (except their geometric setup) K. Li, N. Bevins, J. Zambelli, G.-H. Chen, Med. Phys. 40, p (013) 11

12 Method A: Image-based approach 1. Calculate the NPS of absorption CT. Scale the NPS of absorption CT by the ratio of C g / f Subject to errors caused by aliasing Method B: Projection-based approach 1. Scale the absorption projections by a factor of. Reconstruct DPC-CT using these scaled absorption projections 3. NPS calculation Immune to aliasing 1

13 f z f x f y C g f Absorption CT NPS w/o gratings DPC-CT NPS (predicted) DPC-CT NPS (Measured) Magnitude of Difference K. Li et al. SPIE 8668, Medical Imaging

14 f z f x f y f C g DPC-CT NPS Absorption CT NPS (predicted) Absorption CT NPS (Measured) Magnitude of Difference 14

15 Measured Predicted -6 x x Absorption CT f z (mm -1 ) f z (mm -1 ) f x (mm -1 ) f x (mm -1 ) -6 x x DPC-CT f z (mm -1 ) f z (mm -1 ) f x (mm -1 ) f x (mm -1 ) 15

16 DPC tomosynthesis reconstructed by shift-and-add Absorption Projections 1. Scale by 3D NPS f z Predicted f x. DPC Recon f y DPC Projections DPC Recon 3D NPS f z Measured f x f y K. Li, J. Garrett, Y. Ge, G.-H. Chen, Wednesday 4:50, Room

17 DPC tomosynthesis reconstructed by FBP Absorption Projections 1. Scale by 3D NPS f z Predicted f x. DPC Recon f y DPC Projections DPC Recon 3D NPS f z Measured f x f y K. Li, J. Garrett, Y. Ge, G.-H. Chen, Wednesday 4:50, Room

18 We considered the five commonly used model observers in x-ray absorption imaging: Ideal observer Non-prewhitening (NPW) observer Non-prewhitening observer with eye filter and internal noise (NPWEi) Prewhitening observer with eye filter and internal noise (PWEi) Channelized Hotelling Observer (CHO) (with Gabor basis functions) 18

19 Absorption CT DPC-CT Noise-only image D noise power spectrum (NPS) Zambelli, et al. Proc. SPIE, 7961, p79613n (011) 19

20 A model observer should predict human performance, but each model observer will behave differently. This then motivates the following question: Given the peculiar noise power spectrum in DPC tomographic imaging, which model observer should be used to assess the performance of DPC imaging? 0

21 1. Detection of circular object. Detection of breast lesion* 8 pixels (0.64 mm) 16 pixels (1.8 mm) 3 pixels (.56 mm) 64 pixels (5.1 mm) 18 pixels (10.4 mm) Original Segment, MTF blurring *N. Prionas, et al., Radiology, 56, p714 (010) Breast CT data courtesy of John Boone 1

22 AFC: two-alternative forced-choice SKE: signal-known exactly The ground truth (lesion size and shape) and circular cues (lesion location) were provided to the observers Left or right? (you must choose one)

23 Four physicist observers Each read 56 trials x 7 tasks (5 discs, breast lesions) Training session prior to actual trial Monochrome diagnostic quality monitor (Coronis 5MP Mammo, Barco Inc.) Responses recorded by mouse/keyboard input 70 cm viewing distance W/L: [mean-4σ, mean-4σ] Dark reading room 3

24 Contrast Human observer A Human observer B Human observer C Human observer D Detail (pixels) Inter-observer variation< 5% 4

25 log(contrast) DPC CD curve: Human (Mean) y=mx+b fitting detail contrast Slope = -0.5 R = log(detail) K. Li et al. SPIE 8668, Medical Imaging

26 Contrast Human Observer NPWEi Ideal CHO Observer Detail (pixels) 6

27 Contrast threshold Contrast threshold Lesion 1 Lesion Human NPW NPWEi PWEiCHO (Gabor) 0.45 Human NPW NPWEi PWEiCHO (Gabor) 7

28 Signal Model Observer Ideal NPW NPWEi PWEi CHO Disc (d=8) [-7%, 7%] [-16%, 16%] [-81%, 81%] [-17%, 17%] [-9%, 9%] Disc (d=16) [-71%, 71%] [-11%, 11%] [-19%, 19%] [-13%, 13%] [-10%, 10%] Disc (d=3) [-7%, 7%] [-13%, 13%] [-9%, 9%] [-9%, 9%] [-9%, 9%] Disc (d=64) [-7%, 7%] [-1%, 1%] [-9%, 9%] [-9%, 9%] [-9%, 9%] Disc (d=18) [-75%, 75%] [-3%, 3%] [-0%, 0%] [-17%, 17%] [-11%, 11%] Lesion 1 [-39%, 39%] [-9%, 9%] [-9%, 9%] [-9%, 9%] [-9%, 9%] Lesion [-53%, 53%] [-18%, 18%] [-15%, 15%] [-16%, 16%] [-11%, 11%] 8

29 DPC-CT or DPC-Tomo imaging does not need new image quality metrics; existing performance metrics from x-ray absorption imaging can be directly applied; Given x-ray absorption imaging performance and grating quality factors (visibility and transmission rate), one can quantitatively determine the corresponding performance of a corresponding DPC imaging system for grating based DPC imaging system. The model observer method can be used to predict human performance for relatively simple SKE tasks; Among all model observer investigated in this study, CHO model yields the best overall agreement with human observer performance. 9

30 Using model observer performance as a metric to optimize DPC imaging system; Determine the pros and cons for DPC imaging system for a given clinical task and radiation dose constraint. 30

31 Dr. Zambelli, Dr. Bevins, John Garrett Physicist observers who participated in the human observer experiments 31

32 Thank You e UW CT Research gchen7@wisc.edu 3

33 Local NPS (mm ) Basic requirement System is linear and shift-invariant DPC imaging system meets this requirement Because it does not require any non-linear stage to be added to the imaging chain Example: Experimental demonstration of noise stationarity C B A E D Region A Region B Region C Region D Region E 10 0 Spatial frequency f (cycles/mm) 33

34 Absorption projections DPC projections Ramp ab T1 f 1. Filtering Modified Hilbert T p sgn( f ) d dpc 1 e.g., de-noise filter. Additional Filtering e.g., de-noise filter T f x ab 3 sinc ( ) for bilinear 3. Interpolation T f x dpc 3 sinc ( ) for bilinear T ab 4 M n 1 f or projection matrix 4. Backprojection T dpc 4 M n 1 f or projection matrix Convolution with the 3D comb 5. Resampling Convolution with the 3D comb Absorption CT images NPS NPS T T T T ab ab ab ab ab ab CT proj DPC CT images NPS NPS T T T T dpc dpc dpc dpc dpc dpc CT proj D. Tward and J. Siewerdsen, Med. Phys. (008) K. Li, N. Bevins, J. Zambelli, G.-H. Chen, Med. Phys. (013) 34

35 NPS of Absorption CT NPS of DPC CT NPS NPS T T T T ab ab ab ab ab ab CT proj NPS NPS T T T T dpc dpc dpc dpc dpc dpc CT proj NPS dpc proj NPS ab proj NPS of Absorption CT NPS of DPC CT NPS NPS T T T T ab dpc ab ab ab ab CT proj NPS NPS T T T T dpc ab dpc dpc dpc dpc CT proj

36 Experimental D axial DPC-CT noise images Acquired from a benchtop DPC-CT system 80 µm pixel size 360 x 360 image matrix size Digital signals were blurred by the system MTF before being added to the experimental noise background 36

37 Responses from the AFC experiments generated the portion of correct response (P c ), which is related to the model observer d by P c 1 d ' 1 erf, where x t erf(x) e dt 0 To minimize sampling errors due to the finite number of trails, the expected value of P c should be close to 9% in AFC experiments* * A. Burgess, Med. Phys.,, p643 (1995) 37

38 In order to get an P c close to 9% for each task Two contrast levels to achieve P c [88%, 9%] and P c [9%, 96%] were determined by training trail results The AFC experiments were repeated at each of the two contrast levels to get two P c values The contrast threshold to achieve P c = 9% was determined by linear interpolation P c?% 9%?% C H C C L Contrast A. Burgess et al., Med. Phys. 8, p419 (001) 38

39 Error bars of human results: Sampling error Pc(1 Pc) ( Pc ) N Error bars of model observer results: Uncertainty in the NPS/covariance measurement (measured using bootstrapping)* Results were reported as contrast-detail curves x-axis: Object size (in pixels) y-axis: Contrast threshold to achieve 9% P c * I. Reiser and R. Nishikawa, Med. Phys. 37 (010) 39

40 Ke Li, et al, Phys. Med. Biol. (013) 40