https://en.wikipedia.org/wiki/Lulu_smoothing
I'm interested in using this approach to remove signal spikes from an analog sensor connected to a microcontroller. I understand the L and U operations, however the Wikipedia page fails to indicate how these two results would be combined.
Is the resulting dataset from L fed into U (or vise versa for UL). IE L(U(dataset))?
Rohwer's original paper, "Idempotent one-sided approximation of median smoothers" (1989), appears to be available online as open access. It applies operators on the left, so $L_nU_nx$ means apply $U_n$ to the sequence $x$ and then apply $L_n$ to the result.
(The figures on Wikipedia are inconsistent with Rohwer's notation.)