We introduce a novel, computationally efficient model preconditioner, the guided filter, a multi-dimensional, structure-oriented, and edge-preserving filter, with a selfadjoint implementation which does not require a priori knowledge of the structural dip field. We show how to generalize the guided filter to higher dimensions, so that it may be used on typical 3D models and seismic images. We also provide proof that the guided filter is self-adjoint and show applications of the guided filter to seismic reflection tomography.

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