A Two-stage Signal Decomposition into Jump, Oscillation and Trend using ADMM

We present a thorough implementation of the two-stage framework proposed in [A. Cicone, M. Huska, S.H. Kang and S. Morigi, JOT: a Variational Signal Decomposition into Jump, Oscillation and Trend, IEEE Transactions on Signal Processing, 2022]. The method assumes as input a 1D signal represented by a finite-dimensional vector in RN . In the first stage the signal is decomposed into Jump (piece-wise constant), Oscillation, and Trend (smooth) components, and in the second stage the results are refined using residuals of other components. We pro-pose an efficient numerical solution for the first stage based on alternating direction method of multipliers, and a solid algorithm for the solution of the second stage.