# Retrospective motion correction for structural MRI

Good quality results can only be obtained with good quality images. To obtain images with good SNR and high resolution, long scan times are often necessary. However, with longer acquisition, the subjects are more likely to move. Rather than acquire a very long sequence, that often can last up to 40 minutes, the acquisition can be broken into many shorter scans, each with lower SNR. These are coregistered, effectively reducing the effect of undesired movement, and averaged, for increase of the SNR (Kochunov et al, 2006).

The last image in the second row is the average of all the other seven, after retrospective motion correction has been applied.

The results above are typical. Each pixel above corresponds to a true voxel, with no interpolation. Therefore, to see in more detail, simply download the image above and use an image viewer (e.g. gwenview or eog) to zoom.

The method is termed retrospective to discern it from prospective motion correction methods, such as those available for BOLD-sensitive EPI acquisitions (e.g. Siemens 3D PACE).

Since the images belong to the same subject and typically the movement is of only a few degrees or milimeters, the affine matrices for these corrections should have a diagonal with values very close to 1 and very close to zero off the diagonal. Here is one example:

0.999995    -0.00020007  -0.0030414    0.106906
0.000188555  0.999993    -0.00378601   0.100499
0.00304214   0.00378542   0.999988    -0.204133
0            0            0            1

As usual, the improvement in the SNR is given by a factor of $\sqrt{n}$, where $n$ is the number of images averaged.