The need of analysis of irregularly sampled data arises from many scientific disciplines, such as astronomy and astrophysics, geoscience and seismics, oceanography, telecommunications, remote sensing and medical imaging. The analysis of this kind of data is more complicated than the one of regularly sampled data. Therefore a common approach is to resample the irregular data on a regular grid.
It is however of interest to explore the possibility of analytical tools capable of dealing directly with irregularly sampled data.
In linear Image Processing, an ubiquitous operation is that of convolution of an input signal p(t) with a filter g(t), such that the output signal y(t) produced by the convolution 
highlights particular characteristics of the original input signal. The convolution can be simplified to a multiplication 
using the Fourier transform. The investigation of the Fourier transform in the case of irregularly sampled input signal is therefore of great interest, since the knowledge of the Fourier transform in the irregular sampling case allows one to perform convolution in the irregular case and therefore opens the possibility of performing linear Image Processing on irregularly sampled signals.