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Appendix A: Summary of the proposed properties of the Imaging Model

The Imaging Model is a class with the following services:

predict: returns AI for given I,
solve: returns A^TwD for given D, optionally normalized by the diagonal elements of A^TwA (if A^TwA is diagonal, the normalized version is the solution to the normal equation),
residual: returns (AI - D)^Tw(AI - D) and A^Tw(AI - D) for given I and D, optionally normalized by the diagonal elements of A^TwA,
observe: returns A^TwAI for given I, optionally normalized by the diagonal elements of A^TwA,
Hdiagonal: returns the diagonal elements of A^TwA.

One could imagine defining a special Imaging Model such that the matrix A is supplied explicitly in the constructor. These various services would then be realized by actually calling the relevant Math routines. It is anticipated that only in the rare simple cases will any of these operations be implemented using simple matrix algebra. In general, special properties of the matrix A must be used to make the computation feasible. Hence the Imaging Model could be regarded as related to the Matrix class but with only some operations allowed.

In current AIPS++ terms, D is a YegSet and I is an Image.

Up: Recommendations for the AIPS++ Imaging Model Previous: References