A computer-implemented method to correct motion and interpolation effects for functional magnetic resonance imaging (fMRI) analysis is provided. The method estimates the motion on every voxel of the data and removes those effects to leave a residual signal that can be analyzed to high accuracy. The estimation of the motion includes solving a normal matrix equation based on the local translational motion of each voxel of the head, and a regularization parameter that depends on the local spatial structure of the head. Methods to regularize a matrix from the normal equation using the regularization parameter are also provided. A rolling filter implementation for real-time processing and motion correction is provided.