Consider uniformly-spaced samples of smooth, bandlimited signal observed in noise and subject to some artifacts (small jumps). Physical restrictions impose a constraint on the maximum magnitude of the derivative of the noiseless, "artifactless" signal. In an effort to smooth the signal and remove artifacts, I could impose this constraint by simply limiting the size of the sample-to-sample change (e.g., matlab, but this seems like it will introduce other effects to compromise the smoothness of the signal.
The only other option I came across are nonlinear feedback loops (e.g., see this paper. I suppose that one could also impose derivative inequality constraints on, say, some local polynomial representation of the signal as well. Any other ideas, references, etc?