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Shift-and-add refers to a speckle suppression technique that is commonly used in astronomy, where it is effective, inexpensive and conceptually simple. It is used in telescope observation to increase the quality of the resulting images, by amateur and professional astronomers for telescopes of all sizes. It can be thought of as making a video of the intended target, then, in order to compensate for the apparent shifting of the observed target due to the constantly-changing seeing issues of the atmosphere (pockets of air with certain characteristics acting as a distorting lens), if in one video frame, the stars are one pixel to the left of where it was before, just shift that frame one pixel to the right to line them up again (or whatever the number of pixels in whatever direction), finally summing the data for all these frames: instead of a bunch of dim images, you have a brighter image but without some of the blurring due to short-term atmospheric distortions. Finding the alignment is particularly assisted in astronomy by the fact that fields generally include stars, which are point sources, making it easy to find locations within the image to be lined up. Though my description uses the word "video", the technique still benefits even at a considerably slower frame rate, and any rate faster than the typical changes in such atmospheric disturbances gains much of the possible benefit. CCDs, organizing the images as pixels, make the technique straightforward, and as long as you have the means to save individual images taken successively and load them into a computer, software can carry out the shift-and-add operation, i.e., no specialized equipment is necessary.
In many cases, shift-and-add is the default method of speckle suppression. More sophisticated methods may use probabilistic calculations to decide exactly how to line up the images, and may accommodate the notion that different regions of the image might be distorted in different directions.
The same general shift-and-add technique is used for the image stabilization feature of some cameras, which use essentially the method to compensate for slight movements of the camera while taking a picture.
Shift-and-add may be thought of as a particular kind of image stacking.