We present a novel methodology able to distinguish meaningful level shifts from typical signal fluctuations. A two-stage regularization filtering can accurately identify the location of the significant level-shifts with an efficient parameter-free algorithm. The developed methodology demands low computational effort and can easily be embedded in a dedicated processing unit. Our case studies compare the new methodology with current available ones and show that it is the most adequate technique for fast detection of multiple unknown level-shifts in a noisy OTDR profile.

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Identifying the unknown underlying trend of a given noisy signal is extremely useful for a wide range of applications. The number of potential trends might be exponential, thus their search can be computationally intractable even for short signals. Another challenge is the presence of abrupt changes and outliers at unknown times which impart resourceful information regarding the signal's characteristics. In this paper, we present the 1 Adaptive Trend Filter, which can consistently identify the components in the underlying trend and multiple level-shifts, even in the presence of outliers. Additionally, an enhanced coordinate descent algorithm which exploits the filter design is presented. Some implementation details are discussed and a version in the Julia language is presented along with two distinct applications to illustrate the filter's potential.