Selected topics on fmri image processing

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1 fmri Symposium, 24 January, 2006, Ghent Selected topics on fmri image processing Jan Sijbers

2 The fmri folks of the Vision Lab UZA Bio-Imaging Lab Vision Lab Univ. Maastricht T.U. Delft 1

3 Overview generalized likelihood ratio tests for fmri data resolution improvement of fmri activation maps temporal clustering of fmri data registration of cortices 2

4 Construction of generalized likelihood ratio tests Application to fmri J. Sijbers A. J. den Dekker D. poot

5 Some statistical terms test statistic & threshold null hypothesis H 0 prob. of false alarm: P f prob. of detection: P d alternative hypothesis H 1 4

6 Likelihood ratio test Joint PDF: parameter vector vector of observation variables Sir R. Fisher Likelihood function: Likelihood ratio: likelihood under H 1 likelihood under H 0 The LR compares the likelihood under H 1 with the likelihood under H 0. 5

7 Generalized likelihood ratio test Replace the unknown parameters in the likelihood ratio by their maximum likelihood estimates: with GLRT principle: reject H 0 if where can be chosen such that the false alarm rate. with the GLRT is uniformly most powerful among all tests. 6

8 Literature Steven Kay: Fundamentals of statistical signal processing 7

9 Application to low SNR fmri signal processing

10 fmri experiment 9

11 Magnitude, Phase, Real, Imaginary real imaginary magnitude 2 A = R + I 2 phase ϕ = arctan I R 10

12 Magnitude fmri data Data Parameters Model 11

13 GLRT for magnitude fmri data Likelihood functions under H 0 and H 1 : GLRT statistic: where 12

14 HIGH SNR (>10) LOW SNR 13

15 Magnitude, Phase, Real, Imaginary R I = = Acosϕ Asinϕ phase real imaginary A = ϕ = R 2 + arctan I I R 2 magnitude magnitude phase 14

16 Complex fmri data Data Parameters Model 15

17 Votes of the GLRT jury 16

18 Conclusions one day, you might want to build your own statistical test when this day comes... remember the GLRT be careful with low SNR fmri data - statistics may be non-gaussian - if possible... don t throw away the phase... future work - include temporal and spatial correlation 17

19 Wavelet-based enhancement of image series using an auxiliary image P. Scheunders S. De Backer A. Duijster

20 Introduction: Image series 19

21 Introduction: Image series 20

22 Introduction: Image series 21

23 Introduction: Image series 22

24 Introduction: motivation Image Enhancement: Spatial Resolution SNR Image series: Trade-off -SNR - Spatial Resolution - Spectral (time) Resolution X = G S + N 23

25 Introduction: motivation Remote Sensing: Panchromatic image image fusion Functional MRI: Anatomical image image registration, interpretation 24

26 The dyadic wavelet representation ψ x θ( x, y) y θ( x, y) ( x, y) = ψ ( x, y) = x y x 1 x x y y 1 y x y ψ s ( x, y) = ψ (, ) ψ (, ) (, ) 2 s x y = ψ 2 s s s s s s x x y y s s s s D ( x, y) = I ψ ( x, y) D ( x, y) = I ψ ( x, y) θ(x,y) is a smoothing function s = 2 j 25

27 The dyadic wavelet representation 26

28 The dyadic wavelet representation 27

29 Wavelet-based Bayesian Estimation Wavelet coefficients x : observed image series; s : ideal y : auxiliary single - band image image series Assume that - y is of optimal spatial resolution and noise-free - all pdf s are normally distributed - s and y are jointly normally distributed sˆ = argmax s p( s x, y) p( s x, y) ~ p( x s) p( s y) 28

30 Results 29

31 Results 30

32 Results 31

33 Results 32

34 Results 33

35 Results 34

36 Conclusions Framework to enhance image series, using an auxiliary image. Multiscale, using wavelet transform Bayesian framework, using Gaussian models Further work: - Better models: Gaussian Scale Mixture model - Medical validation, link between enhancement and activation detection in fmri. 35

37 Fuzzy Clustering Time-Resolved fmri-data: tracing spatiotemporal patterns of cortical activation during audiospatial mental imagery A. Smolders F. De Martino E. Formisano J. Sijbers P. Scheunders

38 Experiment description Stimuli : visually displayed or auditory instructed sequence of segments, building up figure Jittered delay Presentation of target figure (rotated over certain angle) Task : comparison and decision if identical or mirror-inversed Goal : Fuzzy Clustering Method to trace both topography and sequence of cortical activations across brain regions. 37

39 Auditory 38

40 Imagery 39

41 Visual 40

42 imagery Mixture :? and imagery? (vessel) vessel Flat map auditory mixture : vis., imag auditive, vessel visual 41

43 Registration of cortices T. Huysmans J. Sijbers B. Verdonk

Corresponding Human Cortices two cortices - initial: spherical parameterization - improve: non-linear registration on sphere n cortices: use two cortices -algorithm - correspond

44 Corresponding Human Cortices two cortices - initial: spherical parameterization - improve: non-linear registration on sphere n cortices: use two cortices -algorithm - correspond with arbitrary cortex - calculate mean of n cortices - correspond with mean cortex applications - variability studies - fmri activation visualization - fmri activation statistics 43

45 Corresponding Human Cortices: spherical parameterization 1. collapse edges 2. map base mesh 3. split + optimize vertices 44

46 Corresponding Human Cortices: curvature as registration feature 45

47 Corresponding Human Cortices: curvature as registration feature 46

48 Future work: Tractography + fmri A. Leemans W. Van Hecke J. Sijbers P. Parizel 47

49 Thanks to your brain for listening

The organization of the human cerebral cortex estimated by intrinsic functional connectivity

1 The organization of the human cerebral cortex estimated by intrinsic functional connectivity Journal: Journal of Neurophysiology Author: B. T. Thomas Yeo, et al Link: https://www.ncbi.nlm.nih.gov/pubmed/21653723