0
$\begingroup$

I have been reading this paper on MRI and I only do have novice level signal processing insight. I could not understand the following model:

The displacement field (i.e. d) is modelled as a linear combination of basis warps i.e.,

$ \mathbf d=[\mathbf B_1 \mathbf B_2 ........ \mathbf B_{m_x m_y m_z}] \mathbf b$

Where each vector $\mathbf B_i$ is an unravelled version of one basis function from a truncated 3D discrete cosine transform and $m_x, m_y, m_z$ are the order of transform in the $x-, y-, z-$ directions, respectively.

$\endgroup$
  • $\begingroup$ Hi! Yeah, so this is a bit of a non-trivial text, and I don't think I've encountered the term "basis warp" so far; I'm afraid without you asking a specific question and without a lot of context, we have nothing to answer :( $\endgroup$ – Marcus Müller Feb 8 at 18:14
  • $\begingroup$ The displacement field given here is a function that gives the geometric distortion. In MRI, one encodes each voxel with a frequency and phase, then you apply spectral analysis in order to recover the voxel-wise magnitude. When you have eddy-current or susceptibility inhomogenity, phases and frequencies deflect and therefore reconstruction is erroneous. So maybe "basis warp" term is related with this warp of phase and frequency of individual voxels $\endgroup$ – starhd Feb 8 at 18:17
  • $\begingroup$ @MarcusMüller You are right. So let me ask this one: what does each column of B represent? It would be great if explained in a more intuitive way than this paper :) $\endgroup$ – starhd Feb 8 at 19:15

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.