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Prolate Spheroidal Wave Functions for Radio Astronomical Source Modeling

Submitter: Parisa Noorishad and Sarod Yatawatta
Description: Prolate Spheroidal Wave Functions (PSWF) provide an accurate and efficient method of source modeling in radio astronomy. This is of great importance for high fidelity, high dynamic range imaging with new radio telescopes as well as conventional ones. But the construction of PSWF is computationally expensive compared to other closed-form basis functions, although it leads to a more accurate source modeling.

The image of today presents our suggested solution for reducing its computational cost without loss of information.

We propose the use of Delaunay triangulation with different scales (as opposed to regular gridding) of an image during the construction of the matrix kernel which relates the image domain to the visibility (or Fourier) domain. This allows us to do a finer selection of the region of interest (ROI) i.e. the boundary by which a source is recognized in an image, during the PSWF kernel construction. Once the PSWF basis is constructed using the irregular grid, we revert back to the regular grid by interpolation and thereafter, conventional imaging techniques can be applied.

The analysis in [1] has shown that a significant amount of information is conserved, and that the optimality of the source modeling method is not affected by the triangulation scales. It has also been shown that the choice of triangulation scales can be made in such a way to minimize numerical errors for further computation in the image processing.

Further improvement will focus on finer selection of the ROI depending on the source structure, such that an area with higher intensity is represented with more triangle pixels.

[1] http://arxiv.org/abs/1111.0189
Copyright: Parisa Noorishad and Sarod Yatawatta
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