SELECTION OF A CONVOLUTION FUNCTION FOR FOURIER INVERSION USING GRIDDING

In fields ranging from radio astronomy to magnetic resonance imaging, Fourier inversion of data not falling on a Cartesian grid has been a problem. As a result, multiple algorithms have been created for reconstructing images from non-uniform frequency samples. In the technique known as gridding, the data samples are weighted for sampling density and convolved with a finite kernel, then resampled on a grid preparatory to a fast Fourier transform. This paper compares the utility of several convolution functions, including one that out-performs the "optimal" prolate spheroidal wave function in some situations.