Abstract
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 R^N. 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 propose 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.
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