My take, pondering gmic.cpp and the paper.
lookup increment: Speed, in pixels, by which to shift a search window to a new candidate patch. See the technical reference in @David_Tschumperle March 24 post 4 in this thread. In particular, consider Figure 2c. Searching takes place in a rather large lookup area (green box); the algorithm shifts a search window (small blue box) and tests the candidate patch for the likelihood of being a good match for the target area (small red box). If the likelihood is poor, the algorithm shifts the search area by an amount controlled by the lookup increment. One may set a higher lookup increment (default is one pixel) to speed up the search rate, but this comes at an increased likelihood of “skipping over” a good candidate.
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