The question is about imaging with subpixel resolution, or
super-resolution.  How is it done is computer document scanners? 
Described in the literature are such methods as shift-and-add,
interlacing, a middle ground between the two – “drizzle”.  There are
lots of iterative methods that basically do “shift and subtract” and
apply effort to reduce the effect of noise and shift errors.  Of
interest are methods of choice for practical applications where the
shift is well defined, such as in computer scanners.