Once the estimate is a good representation of the observed images,
CR hits can easily be identified on the correction factor
before the
convolution and Eq. (1) can be modified to
The effect will be that there are ``holes'' in the final
correction factor image, which are of the shape of negative PSFs
for single pixel events. Those holes can overlap due to close
CR hits either on the same image or on different images. The
holes in the correction factor from each image can
easily be modeled by creating masks at the CR removal stage
which are unity everywhere but at the position of the CR hit,
where they are zero. From those masks, the holes are computed
Those holes can be filled by locally increasing the weight of the images not affected by the CR hit. If the PSF is well sampled, not all information about the affected pixels is lost because the information contents in neighboring pixels is not independent. This information can also contribute to fill the flux holes. In general, Eq. (2) can be changed to
where the weights now depend on the position in the
image and are computed from
In the special case that there are no CR events on any input image,
equals
everywhere and the method reduces to the original
co-addition scheme.
The only problem left is to find an initial model of the image good enough to allow easy identification of the CR hits. If more than two input images are available, the original co-addition without CR removal but using the scaled medium rather then the sum of the individual correction factors can be used. If only two images are available, the minimum of the two correction factors should suffice. In either of those cases, the full CR treatment as described above only when the model is a good presentation of the observed images.