Optimal gridding and degridding in radio interferometry imaging

In radio interferometry imaging, the Fast Fourier transform (FFT) is often used to compute maps from visibility data. A gridding procedure for convolving the measured visibilites with a chosen gridding function is used to transform visibility values into uniformly sampled grid points. We propose here a parameterised family of ‘least-misfit gridding functions’ which minimise an upper bound on the difference between the DFT and FFT dirty images for a given gridding support width and image cropping ratio. When compared with the widely used spheroidal function with similar parameters, these provide more than 100 times better alias suppression and RMS misfit reduction over the usable dirty map. We discuss how appropriate parameter selection and tabulation of these functions allow for a balance between accuracy, computational cost and storage size. Although it is possible to reduce the errors introduced in the gridding or degridding process to the level of machine precision, accuracy comparable to that achieved by CASA requires only a lookup table with 300 entries and a support width of 3, allowing for a greatly reduced computation cost for a given performance.

On a General Class of Multiple Eulerian Integrals with Multivariable I-Functions

Recently, Raina and Srivastava and Srivastava and Hussainhave provided closed-form expressions for a number of a Eulerian integral involving multivariable H-functions. Motivated by these recent works, we aim at evaluating a general class of multiple Eulerian integrals concerning the product of two multivariable I-functions defined by Prathima et al. [6], a class of multivariable polynomials and the spheroidal function. These integrals will serve as a capital formula from which one can deduce numerous integrals.