Windowed locally monotonic regression

Lomotonicity, the largest degree of local monotonicity that a signal has, is proposed as an appropriate measure of smoothness when studying smoothers such as the median filter. Locally monotonic regression (LMR) optimally solves the problem of smoothing a signal to a specified minimal degree of lomotonicity, but it often requires an excess of computational resources. Windowed locally monotonic regression (WLMR) presents an attractive alternative to the problem of smoothing signals under the smoothness criterion of lomotonicity. This criterion is meaningful, for example, when processing images and speech signals. Unlike LMR, WLMR is defined also for infinite-length signals; this may be useful in more theoretical studies of this tool