L1AdaptiveTrendFilter.jl is a Julia package for filtering and identifying unknown underlying trends of a given noisy signal. It is originally a supplemental material for our paper "L1 Adaptive Trend Filter via Fast Coordinate Descent".


In order to use it, download the package in the julia prompt with the command:


Then simply include the command using L1AdaptiveTrendFilter to import the package.


The function l1_adaptive_trend_filter performs the filtering via coordinate descent and takes the following required inputs:

  • y : Signal or time-series to be filtered; (Must be a vector of reals)
  • components: List of integers corresponding to the types of components to be considered. (must be a vector of integers containing some of the following numbers: 1 = Step, 2 = Spike, 3 = Slope, 4 = Sine, 5 = Cossine )

Optional inputs:

  • f: Vector of overcomplete frequencies (Default=ø);
  • numλ: Size of the regularizer path for the parameter λ (Default=40);
  • numγ: Size of the regularizer path for the parameter γ (Default=10);
  • MAXITER: Maximum number of iterations (Default=500);
  • verbose: Boolean flag for displaying progress of algorithm (Default=false);
  • lower_bounds: List of lower bounds for each component type (Default=[-∞,-∞,-∞,-∞,-∞]);
  • upper_bounds: List of upper bpunds for each component type (Default=[+∞,+∞,+∞,+∞,+∞]).

This function returns:

  • β_path: Path of components coefficients;
  • y_path: Path of filtered signals;
  • β_best: Best components coefficients according to the EBIC criteria;
  • y_best: Best filtered signal according to the EBIC criteria;
  • λ_best: Best value for the λ regularizer according to the EBIC criteria;
  • γ_best: Best value for the γ regularizer according to the EBIC criteria.


# after initializing the package with
# Pkg.clone("git://github.com/joaquimg/L1AdaptiveTrendFilter.jl.git")

#You must include the library with:
using L1AdaptiveTrendFilter

y = rand(18) # some inputs
components = [1,3] #(meaning we only consider step and slope components)

# run the algorithm
beta_path, y_path, beta_best, y_best, lambda_best, gamma_best = l1_adaptive_trend_filter(y,components)


one option is to remove the package and add it again:


Citing this package

Please use the following Bibtex reference:

  title={$$\backslash$ ell\_1 $ Adaptive Trend Filter via Fast Coordinate Descent},
  author={Souto, Mario and Garcia, Joaquim D and Amaral, Gustavo C},
  journal={arXiv preprint arXiv:1603.03799},

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