Image reconstruction from frequency domain data on arbitrary contours

This paper presents a new view of the problem of image reconstruction in the spatial Fourier domain based on the generalized projections of a two-dimensional image. The algorithms that are presented are derived from the exact continuous relations between the Fourier transforms of a spatially limited image and those of its generalized projections. A Fourier domain reconstruction formula is derived that is a natural consequence of these relations giving values of the two-dimensional transform on a regular grid useful for inverse FFT. This approach is contrasted with the more ad hoc methods of Fourier domain interpolation and with the spatial domain approaches such as the backprojection and backpropagation methods.