The core step in LandTrendr processing is the simplification of a time-series of Landsat spectral values into their salient "shape", as represented by successive connected straightline segments.   

Above, we show flow of steps needed to identify straightline segments in a single pixel's spectral trajectory.  Details are given in Kennedy et al. (2010). Briefly, we first eliminate spikes (a), identify possible transition points (vertices) in the time series (b), remove extraneous vertices (c), identify the best path through the vertices (d), then sequentially simplify the time series (e) and finally select the best model using a simple fitting statistic (f).  
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How LandTrendr works

Overall workflow  Pre-processing Segmentation (this page) Mapping Change Mapping Landcover