Time and covariance smoothing for restoration of bivariate signals
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913911986454528 |
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| author | Pilavci, Yusuf Yigit Palud, Pierre Flamant, Julien Thouvenin, Pierre-Antoine Boulanger, Jérémie Chainais, Pierre |
| author_facet | Pilavci, Yusuf Yigit Palud, Pierre Flamant, Julien Thouvenin, Pierre-Antoine Boulanger, Jérémie Chainais, Pierre |
| contents | In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory, called polarization ellipse, is highly informative to solve ill-posed inverse problems involving bivariate signals where the signal is collected through indirect, noisy or incomplete measurements. This work proposes a novel formulation and an efficient algorithm for reconstructing bivariate signals with polarization regularization. The proposed formulation leverages the compact representation of polarization through the instantaneous covariance matrices. To address the resulting quartic optimization problem, we propose a well-suited parameter splitting strategy which leads to an efficient iterative algorithm (alternating direction method of multipliers (ADMM)) with convex subproblems at each iteration. The performance of the proposed method is illustrated on numerical synthetic data experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time and covariance smoothing for restoration of bivariate signals Pilavci, Yusuf Yigit Palud, Pierre Flamant, Julien Thouvenin, Pierre-Antoine Boulanger, Jérémie Chainais, Pierre Signal Processing In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory, called polarization ellipse, is highly informative to solve ill-posed inverse problems involving bivariate signals where the signal is collected through indirect, noisy or incomplete measurements. This work proposes a novel formulation and an efficient algorithm for reconstructing bivariate signals with polarization regularization. The proposed formulation leverages the compact representation of polarization through the instantaneous covariance matrices. To address the resulting quartic optimization problem, we propose a well-suited parameter splitting strategy which leads to an efficient iterative algorithm (alternating direction method of multipliers (ADMM)) with convex subproblems at each iteration. The performance of the proposed method is illustrated on numerical synthetic data experiments. |
| title | Time and covariance smoothing for restoration of bivariate signals |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2506.20237 |