Modal decomposition of astronomical images with application to shapelets

Details Modal decomposition of astronomical images with application to shapelets Modal decomposition of astronomical images with application to shapelets

2004-01-09

arxiv.org/abs/astro-ph/0401160v1

Astronomy and Astrophysics

Astrophysics

12 pages, 17 figures, submitted to MNRAS

Scientific paper

10.1111/j.1365-2966.2004.08180.x

The decomposition of an image into a linear combination of digitised basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitised basis functions, which may be linearly dependent, non-orthogonal and incomplete. It is shown that such circumstances may result even from the digitisation of continuous basis functions that are orthogonal and complete. In particular, digitised shapelet basis functions are investigated and are shown to suffer from such difficulties. As a result the standard method of performing shapelet analysis produces unnecessarily inaccurate decompositions. The optimal method presented here is shown to yield more accurate decompositions in all cases.

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