The irregular sampling problem is concerned with the problem of dealing with signals and images which may be represented by samples on an irregular grid. One of the most frequent problems to solve is the one of reconstruction of the signal from its samples. The NDFT can be used directly for reconstruction. By computing the Fourier coefficients at all required discrete regular frequencies and then Fourier transforming back with the use of the inverse DFT, a kind of interpolation of the irregularly sampled signal can be obtained.
In order to explain this application, let us first examine the problem of reconstruction of a signal from its regular samples with the use of the inverse Fourier transform.