A normal HDR image is made by combining multiple LDR (low dynamic range) images, each one at a different exposure. Fundamentally the images are aligned then the HDR image is made as a kind of weighted average of the images.
I want to do this, and do image averaging at the same time. This means that rather than having one image per exposure I have more than one - so say 2 or 4 or even 16 images at each exposure.
Image averaging reduces noise. It isn’t widely used, in part because it is bother to take multiple shots, deal with the subject moving etc. However, if you are already doing HDR you have bought off on the problems of taking and processing multiple images.
So far no software that I have tried will do HDR merging and averaging together. In general, there are two sorts of responses - either an error message telling me I have accidentally put the files for more than one HDR shot in at the same time. Or, the software just sorts them and takes one from each exposure and ignores the rest.
One approach would be to do the averaging first, but there don’t seem to be good solutions for doing image averaging out there either - EXCEPT for astrophotography, where it is common technique. I have considered trying to use astrophotography software for this, but when I have looked at the manual for the software, the alignment aspect is discussed entirely in terms of stars which of course I don’t have in conventional landscapes.
In principle a panorama stitching program like Hugin could do the averaging aspect. It could even, in principle make the HDR file. I say “in principle” because in my testing so far Hugin complained about the wide range of different exposure and couldn’t align all of the shots. But perhaps I should keep trying.
In general, the kind of image alignment that Hugin does for panorama stitching including a much wilder set of possible image alignments than doing alignment in HDR merging, so its alignment engine should certainly work, but its default settings might be overkill.