An algorithm for multidimensional nonlinear registration is proposed. The deformation field between two elastic bodies is represented by a multi-resolution separable wavelet. Using a progressive approach that reduces algorithm complexity the registration parameters are recovered in a coarse to fine order. A custom wavelet that approximates threefold orthogonality is developed. The performance of the algorithm is evaluated by the alignment of sections from mouse brains. The wavelet registration algorithm demonstrated on average fourfold improvement in section alignment over linear alignment.