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This paper presents an algorithm to transform and reconstruct diffusion-weighted imaging (DWI) data for alignment of micro-structures in association with spatial transformations. The key idea is to decompose the diffusion-attenuated signal profile, a function defined on a unit sphere, into a series of weighted diffusion basis functions (DBFs), reorient these weighted DBFs independently based on a local affine transformation, and then recompose the reoriented weighted DBFs to obtain the final transformed signal profile. The decomposition is performed in a sparse representation framework in recognition of the fact that each diffusion signal profile is often resulting from a small number of fiber populations. A non-negative constraint is further imposed so that noise-induced negative lobes in the signal profile can be avoided. The proposed framework also explicitly models the isotropic component of the diffusion-attenuated signals to avoid undesirable artifacts during transformation. In contrast to existing methods, the current algorithm executes the transformation directly in the signal space, thus allowing any diffusion models to be fitted to the data after transformation.