Images made through a microscope. All subject types.
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No. In-camera pixel shifting collects new information at each sensor pixel for each exposure. Without the shifting, all images have the same information, just with different random pixel noise. Combining several such images by averaging will reduce the noise level, similar to taking a longer exposure at lower ISO. The lower noise level may reveal a little more low-contrast detail, but it will not change the basic resolution of the capture. In contrast, half-pixel shifting gives you up to double the resolution, and even full-pixel shifting gives you true RGB sensing at each pixel position which doubles the raw capture resolution of the R and B channels.Would stacking a few images shot at the same focus depth work out nearly the same as in-camera pixel shifting for higher resolution?
If the image framing is a little unstable, then you do get new information for each exposure even without pixel shifting. In principle that can be exploited to provide a sort of "poor man's super resolution". In practice, I've never seen anybody make that trick work reliably for macro.