Image Quality and Adaptive Imaging

Transcription

1 Image Quality and Adaptive Imaging Matthew A. Kupinski Associate Professor College of Optical Sciences University of Arizona Tucson, Arizona November 7, 2012

2 Introduction Imaging equation The need for objective measures of image quality Task-based assessment of image quality Adaptive and multimodality imaging Summary

3 Imaging Equation g = Hf + n f : Continuous function representing the distribution of the radiotracer n : Noise. Not necessarily additive H : Imaging operating g : Discrete image data

4 Potential methods Qualitative Visual inspection using a single image Visual inspection using a series of images Visual inspection by committee Quantitative Noise, resolution, contrast, etc.

5 CNR

6 CNR

7 CNR

8 MSE (a) (b) (c) (d) (e) (f)

9 Task-based assessment Task-based assessment of image quality Task What is the image to be used for? Observer Who is performing the task? Objects What are you imaging? Measure the ability of the observer to perform the task

10 Task-based assessment Task-based assessment of image quality Task What is the image to be used for? Observer Who is performing the task? Objects What are you imaging? Measure the ability of the observer to perform the task

11 Tasks Classification Signal present vs signal absent Estimation Estimation of cardiac ejection fraction Combined tasks Detection and localization of abnormalities

12 Figures of merit Need a scalar figure of merit for comparisons Detection tasks Area under ROC Curve or SNR Estimation EMSE (not pixel-based!) or Bayes risk Combined EROC analysis

13 Decision Variables t=t(g) T(g) Decision Variable t Image g

14 Decision Variables Signal absent images pr(t H 0 ) 0.35 T(g) Probability Decision Variable t

15 Decision Variables Signal present images pr(t H 0 ) 0.35 T(g) Probability pr(t H 1 ) Decision Variable t

16 Decision Variables Probability pr(t H 0 ) pr(t H 1 ) Decision Variable t

17 Decision Variables D 0 D 1 Probability pr(t H 0 ) pr(t H 1 ) Decision Variable t

18 Decision Variables D 0 D False-positive fraction Probability pr(t H 0 ) True-positive fraction pr(t H 1 ) 0 Decision Variable t

19 ROC Curve Probability Decision Variable t True-Positive Fraction False-Positive Fraction 1

20 ROC Curve Probability Decision Variable t True-Positive Fraction False-Positive Fraction 1

21 ROC Curve Probability Decision Variable t True-Positive Fraction False-Positive Fraction 1

22 Estimation : Parameters to be estimated b (g) : Estimates for image g EMSE = D b 2E g

23 Combined Tasks 1 Probability of Correct Location Guessing Observer False-Positive Fraction 1

24 Task-based assessment Task-based assessment of image quality Task What is the image to be used for? Observer Who is performing the task? Objects What are you imaging? Measure the ability of the observer to perform the task

25 Observers Classification t = T (g) Estimation b = b (g) Combined t = T (g) b = b (g)

26 Ideal Classifier Requires knowing the distributions of the image data Ideal observer maximizes the ROC curve T (g) = (g) = pr(g H 2) pr(g H 1 )

27 Ideal Estimator Posterior mean: PM = d pr( g) ML: MAP: ML = arg max pr(g ) MAP = arg max pr( g) Estimators can be nonlinear in the image data

28 Ideal Observers Require knowledge of the PDF for the data conditioned on the object class! Classification: Estimation: pr(g H i ) pr(g ) pr( g) pr(g )pr( )

29 Ideal Linear Classifier Hotelling observer Computes test statistic t t = w g where w = K 1 g g Harold Hotelling

30 Ideal Linear Estimator Generalized Wiener estimator Computes linear estimate = + W g g where W = K,g K 1 g Norbert Wiener

31 Ideal Linear Observers Require only first- and second-order statistics of the image data Require the inversion of a large covariance matrix

32 Task-based assessment Task-based assessment of image quality Task What is the image to be used for? Observer Who is performing the task? Objects What are you imaging? Measure the ability of the observer to perform the task

33 Objects are continuous functions Nuclear medicine: Object is 3D distribution of radiopharmaceutical; 4D if we consider time variation X-ray imaging: Object is 3D distribution of x-ray absorption and scattering coefficients (vector valued) Written as f(r) or f(r,t) or f

34 Multimodality and Adaptive Imaging Ideal observers Detection Estimation (g) = pr(g H 2) pr(g H 1 ) PM = d pr( g) pr(g H i ) pr( g) pr(g )pr( )

35 Multimodality and Adaptive Imaging Ideal observers Detection Estimation pr(g ) (g) = pr(g H 2) PM = d pr( g) pr(g H 1 ) pr(g H i ) pr( g) pr(g )pr( )

36 Subject Traditional multimodality imaging (polyscopic) f 1 f 2 Modality 1 (e.g., PET, SPECT) Modality 2 (e.g., CT) g 1 g 1 = H 1 f 1 + n 1 g 2 = H 2 f 2 + n 2 Recon 1 Recon 2 f 1 f 2 g 2 Observer Decision Figure of Merit

37 Traditional multimodality imaging pr(g 1, g 2 )= pr(g 1 f 1 )pr(g 2 f 2 )pr(f 1, f 2 )df 1 df 2 Each system has independent noise The objects depend on one another

38 Subject Isoscopic Multimodality Imaging f Dual Energy SPECT g 1 g 2 Recon 1 Recon 2 f 1 f 2 Observer Decision Figure of Merit

39 Isoscopic Multimodality Imaging pr(g 1, g 2 )= pr(g 1 f)pr(g 2 f)pr(f )df Each system has independent noise Each image depends on the same object

40 Subject Adaptive imaging (isoscopic) f Modality 1 Modality 2 g 1 or f 1 g 1 = H 1 f + n 1 g 2 = H 2 (g 1 )f + n 2 Recon 1 (optional) Recon 2 g 1 or f 1 f 2 Observer Decision Figure of Merit

41 Isoscopic Adaptive Imaging pr(g 1, g 2 )= pr(g 1 g 2, f)pr(g 2 f)pr(f )df g 2 g 1 The scout image affects the second acquisition

42 Subject Polyscopic Adaptive Imaging f 1 f 2 CT SPECT g 1 g 2 f 1 Recon 1 Recon 2 f 1 f 2 Observer Decision Figure of Merit

43 Polyscopic Adaptive Imaging pr(g 1, g 2 )= pr(g 1 g 2, f 1 )pr(g 2 f 2 )pr(f 2, f 2 )df 1 df 2

44 Multimodality and adaptive imaging Ideal linear observers g = Hf + n

45 Multimodality and adaptive imaging Ideal linear observers g = H 0 Af + n The effects of the imaging aperture and detector are characterized by H 0 The patient-dependent effects of attenuation and scatter are characterized by A

46 Multimodality and adaptive imaging Ideal linear observers g = H 0 (g s )Af + n The imaging system now adapts itself based on the scout measurements

47 Multimodality and adaptive imaging Ideal linear observers g = H 0 (g s )Af + n w(g s )=K 1 g g s H 0 (g s )Af sig A is the average of the patient-specific portion of the imaging operator w = K 1 g g

48 Multimodality and adaptive imaging Ideal linear observers g = H 0 (g s )Af + n w(g s )=K 1 g g s H 0 (g s )Af sig K g gs = K (noise) g g s + K (sys) g g s + K (obj) g g s

49 Multimodality and adaptive imaging Ideal linear observers g = H 0 (g s )Af + n (g, gs )= + K,g gs K 1 g g s g g(g s ) = + W g g W = K,g K 1 g

50 How to adapt? Heuristic Task-based

51 How to adapt?

52 How to adapt?

53 How to adapt?

54 How to adapt?

55 How to adapt? True positive fraction (TPF) False positive fraction (FPF)

56 How to adapt?

57 How to adapt? Task-based assessment of image quality Task What is the image to be used for? Observer Who is performing the task? Objects What are you imaging? Measure the ability of the observer to perform the task

58 How to adapt? Task-based assessment of image quality Task What is the image to be used for? Observer Who is performing the task? Objects What are you imaging? Measure the ability of the observer to perform the task

59 How to adapt? Generate adaptation strategy for patients that are consistent with the scout data generated

60 How to adapt? pr(f g s )

61 Summary Image quality measures should account for the task, the observer, and the patient population Knowledge of ideal observers helps define the limits of observer performance and can be used for hardware optimizations Adaptive imaging can be accomplished by analyzing patients consistent with the scout data