A Gentle Introduction to Image Processing and Reconstruction in FMRI

Transcription

1 A Gentle Introduction to Image Processing and Reconstruction in FMRI Daniel B. Rowe Program in Computational Sciences Department of Mathematics, Statistics, and Computer Science Marquette University Department of Biophysics Department of Electrical Engineering CCNS Program May 5, 2016 NIHR21 NS

2 Special Thanks To: Tom Witelski, Directorate Liason Hongtu Zhu, Workshop Organizer The SAMSI Directorate & Staff NSF Funding for SAMSI 2

3 FMRI Analysis Lab at Marquette Special thanks to Current PhD students: Ms. Mary C. Kociuba, Marquette University Mr. Kevin K. Liu, Marquette University Current Postdoc: Dr. Ben Risk, SAMSI/UNC and former PhD students: Dr. Andrew S. Nencka, Medical College of Wisconsin Dr. Andrew D. Hahn, University of Wisconsin-Madison Dr. Iain P. Bruce, Duke University Dr. M. Muge Karaman, University if Illinois-Chicago 3

4 MRI Processing WG Session Dan Rowe: A Gentle Introduction to Image Processing and Reconstruction in FMRI Iain Bruce: Quantifying Correlations Artificially Induced in fcmri Data by the SENSE pmri Ben Risk: Examination of Artifacts from Multiband Imaging Mary Kociuba: A Method to Mitigate Inter-Slice Signal Leakage in SMS-fMRI Adam Jaeger: Topology and fmri Data Dan Rowe: The Current State of Image Processing and Reconstruction with Future Directions 4

5 Outline Introduction FMRI & fcmri processed to correct artifacts or reduce noise. Image Reconstruction Voxels are not directly measured (k-space). Reconstructed! Image Processing Images are processed for enhancement & artifact reduction. Implications Effects of image reconstruction & processing? Mean, Var, Corr? Discussion We need to be careful. Other reconstruction procedures. 5

6 Introduction Words of Wisdom: Ideally we should model and analyze the original data that we measure, not a processed version of our data. Don t change the data to fit the model, change the model to fit the data. We should statistically analyze all of our data and not delete half of it for convenience. Favorite Phrase: Analyzed raw preprocessed data. 6

7 Introduction MO TS m t TS Model 2,, Activation 2 tf,, Threshold FWE,FDR,PCE In fmri the statistical analysis (almost) always begins with magnitude-only time series. Big Black Box Big Black Box There is a that is ignored between MO TS model and the physical quantities. 7

8 Introduction MO TS m t TS Model 2,, Activation 2 tf,, Threshold FWE,FDR,PCE Big Black Box Hopefully by not considering black box we don t go down with the ship. 8

9 Introduction MO TS m t TS Model 2,, Activation 2 tf,, Threshold FWE,FDR,PCE Shed Some Light Big Black Box On Inner Workings Hopefully by not considering black box we don t go down with the ship. 9

10 Image Reconstruction (FOV=240 mm) (n x =n y =96, Δx=Δ y=2.5 mm) We inverse Fourier transform spatial freqs to generate image. loc. freq., intensity amp. Cartesian Coordinates + i +i +i = +i IFT matrix spatial frequencies IFT matrix image 10

11 Image Reconstruction (FOV=240 mm) (n x =n y =96, Δx=Δ y=2.5 mm) We inverse Fourier transform spatial freqs to generate image. loc. freq., intensity amp. Polar Coordinates + i +i +i exp(i ) FT matrix spatial frequencies FT matrix Phase discarded. Ask for the other ½ of YOUR data. image 11

12 Image Reconstruction The machine Fourier encodes the image. Measure spatial freq. Illustrative Example loc. freq., intensity amp i +i +i = +i 0 FT matrix image FT matrix spatial frequencies 12

13 R Image Reconstruction We can stack freq. rows of reals over rows of imaginaries, I f 13

14 R Image Reconstruction We can stack freq. rows of reals over rows of imaginaries, make one IFT reconstruction matrix from the two, I O R f f R f I 14

15 R Image Reconstruction We can stack freq. rows of reals over rows of imaginaries, make one IFT reconstruction matrix from the two, v = to get the image rows of reals over rows of imaginaries. I O R f y R f R y I f I 15

16 Image Processing Many processing operations are performed by the scanner, by physicists, and by engineers before statistical analysis. + i k-space Processing Nyquist Ghost Correction Static B0 Field Correction Zero Fill Interpolation Non-Cartesian Interpolation Ramp Sampling Interpolation Homodyne Interpolation Apodization And many more Image Reconstruction 2D inverse Fourier transform In-Plane SENSE/GRAPPA Through-Plane SENSE And many more Image Processing Motion Correction Global Normalization Image Smoothing And many more Time Series Processing Dynamic B0 Correction Slice Timing Filtering/Smoothing Physiologic Regressors And many more Show dark blue. Done dark teal. Empirically dark red. Not red. 16

17 Image Processing We can stack freq. rows of reals over rows of imaginaries, make one IFT reconstruction matrix from the two, to get the rows of reals over rows of imaginaries. v= O I O R O k f y R f R O I O k y I image processing k-space processing f I 17

18 Image Processing v I R k O O O f O k O R k-space Processing Nyquist Ghost Correction Static B0 Field Correction Zero Fill Interpolation Non-Cartesian Interpolation Ramp Sampling Interpolation Homodyne Interpolation Apodization And many more Image Reconstruction 2D inverse Fourier transform In-Plane SENSE/GRAPPA Through-Plane SENSE And many more O I O T Image Processing Motion Correction Global Normalization Image Smoothing And many more Time Series Processing Dynamic B0 Correction Slice Timing Filtering/Smoothing Physiologic Regressors And many more Show dark blue. Done dark teal. Empirically dark red. Not red. 18

19 Implications In statistics, we know the rule that says: If a vector f has a mean δ, and a covariance Γ, O O I O R O k Then y=of has a mean μ=oδ, and a covariance Σ=OΓO T. Then Σ can converted into a correlation matrix R=D -1/2 ΣD -1/2. 1/2 Where D 1/ diag( ). Assume k-space measurements independent so Γ=I. 19

20 Implications Correlation matrix and correlation image x5 image cor(y) = 25x25 correlation matrix x5 correlation image 20

21 Implications Correlation, R=D -1/2 ΣD -1/2. R R R RR IR R R RI II +1-1 H 0 Implications TH=

22 Discussion Care needs to be taken when we obtain data. We should get data in its originally measured form. We should do any required processing ourselves. We should develop models that incorporate processing. We should use all of the data (magnitude and phase). 22

23 Forthcoming Iain Bruce: Quantifying Correlations Artificially Induced in fcmri Data by the SENSE pmri Ben Risk: Examination of Artifacts from Multiband Imaging Mary Kociuba: A Method to Mitigate Inter-Slice Signal Leakage in SMS-fMRI Adam Jaeger: Topology and fmri Data Dan Rowe: The Current State of Image Processing and Reconstruction with Future Directions 23