A Neural Network-Based Method for Affine 3D Registration of FMRI Time Series Using Fourier Space Subsets

In this work, we present a neural network (NN)-based method for 3D affine registration of FMRI time series, which relies on a limited number of Fourier coefficients of the images to be aligned. These coefficients are comprised in a small cubic neighborhood located at the first octant of a 3D Fourier space (including the DC component). Since the affine transformation model comprises twelve parameters, the Fourier coefficients are fed into twelve NN during the learning stage, so that each NN yields the estimates of one of the registration parameters. Different sizes of subsets of Fourier coefficients were tested. The construction of the training set and the learning stage are fast requiring, respectively, 90 s and 2 to 24 s, depending on the number of input and hidden units of the NN. The mean absolute registration errors are of approximately 0.03 mm in translations and 0.05 deg in rotations (except for pitch), for the typical motion amplitudes encountered in FMRI studies. Results with an actual time series suggest that the proposed method is suited to the problem of prospective (in frame) FMRI registration, although brain activation must be simulated, and learned, by the NN.