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Timestamp:
Apr 16, 2010, 12:52:37 PM (16 years ago)
Author:
Paul Price
Message:

Branching to test fix of variance/covariance calculation in ppSub.

The calculations of the variance and covariance are usually straight-forward --- the variance gets scaled by the square of any scaling factor applied to the image, and the covariance may be calculated from a convolution kernel. However, when two images are combined, it's not so straight-forward. The standard rules for the propagation of uncertainty tell us to sum the (full) covariance matrices, but it's not immediately clear how to do this in our model where we've separated the diagonal and off-diagonal elements. I had been summing the variance maps and averaging the covariance pseudo-matrices, but this appears to be robbing us of nearly 1 mag of depth. I've reworked this calculation to be a bit smarter: I normalise the (mean of the) variance maps and the covariance pseudo-matrices to unity, calculate from the normalisations the desired mean variance, sum the normalised variance maps with the appropriate scaling, and average (with weights) the covariance pseudo-matrices. This results in deeper photometry on the diff, but there are still a few things to consider before we put this into production: the effect on Magic and the effect on warp-stack and stack-stack diffs (should probably review stack variance/covariance in the light of this fix).

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