Fig. 4.

Principle of the Gridding-based Direct Fourier 3D Reconstruction algorithm (GDFR). (a) 2D FFT of input projection image. (b) The reverse gridding is used to resample 2D Fourier input image into 2D polar Fourier coordinates. (c) “Gridding weights” are computed as cell areas of a 2D Voronoi diagram on a unit sphere (grey polygons) to compensate for the non-uniform distribution of the grid points. (d) Gridding using a convolution kernel with subsequent 3D inverse FFT yields samples on a 3D Cartesian grid. (e) Removal of weights in real space yields the reconstructed 3D object.