2-D interpolation before aliasing

A traditional method of data interpolation on a regular mesh is a four-step procedure: (1) set zero values at the points to be interpolated; (2) Fourier transform; (3) set to zero the high frequencies; and (4) inverse transform. This is a fine method and is suitable for many applications in both one dimension and higher dimensions. Where the method falls down is where more is needed than simple interlacing--for example, when signal values are required beyond the ends of the data sample. The simple Fourier method of interlacing also loses its applicability when known data is irregularly distributed. An example of an application in two dimensions of the methodology of this section is given in the section on tomography beginning on page .