The invention relates to a method and a device for the processing of medical image data so as to determine output function data (S(k)), situated at grid points (8) of a selected grid, from input function data (I.sub.c (r)) situated at grid points (2, 7) of a Cartesian grid (1, 6). A method of this kind is used, for example in magnetic resonance tomography or computer tomography, so as to calculate arbitrary projections from given function data. The method of the invention includes the following steps: determination of modified input function data (I.sub.c '(r)) by division of the input function data (I.sub.c (r)) by the Fourier transform (c(r)) of a convolution kernel (C(k)), determination of the Fourier transform (S.sub.c '(k)) of the modified input function data (I.sub.c '(r)), and determination of the output function data (S(k)) by convolution of the Fourier transform (S.sub.c '(k)) of the modified input function data with the convolution kernel (C(k)), the convolution kernel (C(k)) being a weighting function for weighting the grid points (2, 7) of the Cartesian grid (1, 6) in conformity with their distance from grid points (8) of the selected grid. The method according to the invention offers essentially a substantial reduction of the calculation time required.