Realignment – Motion Correction

1. Realignment – Motion Correction (gif from FMRIB at Oxford)

2. Statistical Parametric Map Design matrix fMRI time-series kernel Motion correction Smoothing General Linear Model Spatial normalisation Parameter Estimates Standard template Overview

3. Reasons for Motion Correction • Subjects will always move in the scanner • The sensitivity of the analysis depends on the residual noise in the image series, so movement that is unrelated to the subject’s task will add to this noise and hence realignment will increase the sensitivity • However, subject movement may also correlate with the task… • …in which case realignment may reduce sensitivity (and it may not be possible to discount artefacts that owe to motion)

4. Within-subject Registration • Assumes there is no shape change, and motion is rigid-body (i.e. translations/rotations) • The steps are: *Registration - i.e. Optimising the parameters that describe a rigid body transformation between the source and reference images - Reference image can be mean image or first image in session *Transformation - i.e. Re-sampling according to the determined transformation

5. Squared Error Rigid body transformations parameterised by: Translations Pitch Roll Yaw 1. Registration Determine the rigid body transformation that minimises the sum of squared difference between images

6. 1. Registration – Mean Squared Difference • Minimising mean-squared difference works for intra-modal registration (realignment) • Simple relationship between intensities in one image, versus those in the other • Assumes normally distributed differences

7. 1. Registration • Iterative procedure (Gauss-Newton ascent) • Additional scaling parameter • Nx6 matrix of realignment parameters written to file (N is number of scans) • Orientation matrices in *.mat file updated for each volume (do not have to be resliced) • Reslice now or later  each time degrades the image

8. 3D Rigid-body Transformations • A 3D rigid body transform is defined by: • 3 translations - in X, Y & Z directions • 3 rotations - about X, Y & Z axes • The order of the operations matters Roll about y axis Pitch about x axis Yaw about z axis Translations

9. Nearest Neighbour Linear Full sinc (no alias) Windowed sinc 2. Transformation (reslicing) • Application of registration parameters involves re-sampling the image to create new voxels by interpolation from existing voxels • Interpolation can be nearest neighbour (0-order), tri-linear (1st-order), (windowed) fourier/sinc, or in SPM2, nth-order “b-splines”

10. B-spline Interpolation A continuous function is represented by a linear combination of basis functions Nearest neighbour and trilinear interpolation are the same as B-spline interpolation with degrees 0 and 1.

11. Residual Errors after Realignment • Interpolation errors, especially with tri-linear interpolation and small-window sinc • Ghosts (and other artefacts) in the image (which do not move as a rigid body) • Rapid movements within a scan (which cause non-rigid image deformation) • Spin excitation history effects (residual magnetisation effects of previous scans) • Interaction between movement and local field inhomogeniety, giving non-rigid distortion

12. Sources & References & So On… • Rik Henson’s SPM minicourse (where these slides where mostly stolen from) • John Ashburner’s lecture on spatial preprocessing (SPM course USA 2005) • Human Brain Function, 2nd Edition (Edited by J Ashburner, K Friston, W Penny) – mostly chapter 2.