Medical imaging applications of effectively multi-dimensional interpolation

We present an accurate and efficient approach to a broad class of multi-dimensional interpolation problems arising in medical imaging that involve the computation of uniform samples in one coordinate system given uniform samples in a different coordinate system. Specifically, the approach is applicable to problems in which the transformation relating the two coordinate systems can be decomposed into lower-dimensional transformations, some of which an linear. In these situations, the interpolation of uniform samples between the subspaces related by the linear transformations can be performed accurately through efficient Fourier-domain manipulations. The remaining interpolation, between nonlinearly related coordinates, can then be performed by linear or higher-order interpolation. We discuss the application of the approach to a number of medical imaging situations and compare it to multi-dimensional linear interpolation. The approach is found to outperform linear interpolation in a range of applications.