In the current version of 3dDeconvolve, the basis functions for polynomials of order 3 (say) are
1 t t^2 t^3
which are not a good choice. I'm in the process of making some changes to the program, one of which is to use Legendre polynomials instead:
1 x (3*x^2-1)/2 (5*x^3-3*x)/2
where
x is defined over the range
[-1,1] for each contiguous set of time points in the input dataset. These functions are approximately orthogonal, which will improve the accuracy of the numerical solution.
Otherwise, I'm not sure I see a huge difference in using polynomials rather than trig functions. If you feel a need to remove exactly only low frequencies, then trig functions (being pure frequencies) may satisfy that need. There is an argument that there is a lot of low frequency noise in FMRI data, and so removing these frequencies explicitly (say, below 0.01 Hz) is desirable. As far as I know, no one has done a systematic comparison of different baseline removal techniques.
bob cox