Registration of DWI data, unlike scalar image data, is complicated by the need of reorientation algorithms for keeping the orientation architecture of each voxel aligned with the rest of the image. This paper presents an algorithm for effective and efficient warping and reconstruction of diffusion-weighted imaging (DWI) signals for the purpose of spatial transformation. The key idea is to decompose the DWI signal profile, a function defined on a unit sphere, into a series of weighted fiber basis functions (FBFs), reorient these FBFs independently based on the local affine transformation, and then recompose the reoriented FBFs to obtain the final transformed DWI signal profile. We enforce a sparsity constraint on the weights of the FBFs during the decomposition to reflect the fact that the DWI signal profile typically gains its information from a limited number of fiber populations. A non-negative constraint is further imposed so that noise-induced negative lobes in the profile can be avoided. The proposed framework also explicitly models the isotropic component of the diffusion signals to avoid undesirable reorientation artifacts in signal reconstruction. In contrast to existing methods, the current algorithm is executed directly in the DWI signal space, thus allowing any diffusion models to be fitted to the data after transformation.