Abstract
The decomposition of an image into a linear combination of digitized basis functions is an everyday task in astronomy. A general method is presented for performing such a decomposition optimally into an arbitrary set of digitized basis functions, which may be linearly dependent, non‐orthogonal and incomplete. It is shown that such circumstances may result even from the digitization of continuous basis functions that are orthogonal and complete. In particular, digitized 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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