Hi Kangjoo,

No this is not the Friston Voltera expansion of motion parameters with 24 parameters. Let R_t be the (demeaned) six rigid body motion parameters (3 translations, three rotations). The Friston model is

[R_t R_t.^2 R_(t-1) R_(t-1).^2]

NIAK only uses
 
[R_t R_t.^2]

I indeed think this may not be standard. Looks like a more common variant is

[R_t R_(t-1)]

Note that NIAK actually retains 95% energy of [R_t R_t.^2] in a PCA, not the full 12 components. Note also that motion regression is by default used in combination to scrubbing, and regression of motion parameters has only little impact on motion artefacts. See (Power et al 2014) http://www.ncbi.nlm.nih.gov/pmc/articles...

I hope this clarifies the model. If you are interested in exploring more variants, feel free to patch niak_brick_regress_confounds, I will include your changes. I have posted an issue on that, and may get to eventually do it myself, although it's pretty low priority. https://github.com/SIMEXP/niak/issues/93 

Best,

Pierre