The shift-and-add method (more recently "image-stacking" method) is a form of speckle imaging

Speckle imaging

Speckle imaging describes a range of high-resolution astronomical imaging techniques based either on the shift-and-add method or on speckle interferometry methods...

 commonly used for obtaining high quality images from a number of short exposures with varying image shifts. It has been used in astronomy for several decades, and is the basis for the image-stabilisation feature on some cameras. The method involves calculation of the differential shifts of the images. The images are then shifted back to a common centre and added together. This provides an image with higher resolution (higher signal-to-noise at high spatial frequencies) than a conventional long exposure image. A number of software packages exist for performing this, including IRAF

IRAF

IRAF is a collection of software written at the National Optical Astronomy Observatory geared towards the reduction of astronomical images in pixel array form. This is primarily data taken from imaging array detectors such as CCDs...

, RegiStax, Keiths Image Stacker, hugin (open source) and Iris.