Non-parametric characterization of gravitational-wave polarizations

Flamant, Julien; Chainais, Pierre; Chassande–Mottin, E.; Feng, F.; Bihan, Nicolas Le

doi:10.23919/eusipco.2018.8552942

Cited by 4 publications

(4 citation statements)

References 9 publications

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“…7: Rank-12 approximation of the original signal using complex SSA and the pseudo-correlation criterion. Indexes of the grouped pairs are: (1, 12), (2, 8), (3,14), (4,15), (5,17) and (6,20). See pseudo-correlation map on the right-side of Figure 5.…”

Section: Resultsmentioning

confidence: 99%

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Polarized Signal Singular Spectrum Analysis with Complex SSA

Journé,

Bihan,

Chatelain

et al. 2023

ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Section: Resultsmentioning

confidence: 99%

“…Bivariate signals can be found in many fields such as optics [1], [2], seismology [3], [4], gravitational wave astrophysics [5,6] or physical oceanography [7], [8] to name just a few. For such physical applications, the notion of polarization plays a key role: it encodes the geometry of oscillations in the 2D plane.…”

Section: Introductionmentioning

confidence: 99%

Polarized Signal Singular Spectrum Analysis with Complex SSA

Journé,

Bihan,

Chatelain

et al. 2023

ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…Complex-valued time series and vectors have attracted attention lately for their ability to model signals from a broad range of applications including digital communications [1], seismology [2], oceanography [3] or gravitational-waves physics [4] to name just a few. Among the specific features of complex datasets, the notion of properness (or second order circularity [5]), in the Gaussian case, is of major importance as it relates invariance of the probability density function to the correlation coefficients of complex vectors.…”

Section: Introductionmentioning

confidence: 99%

Exact Distribution and High-dimensional Asymptotics for Improperness Test of Complex Signals

Chatelain

Bihan

2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Improperness testing for complex-valued vectors and processes has been of interest lately due to the potential applications of complex-valued time series analysis in several research areas. This paper provides exact distribution characterization of the GLRT (Generalized Likelihood Ratio Test) statistics for Gaussian complex-valued signals under the null hypothesis of properness. This distribution is a special case of the Wilks's lambda distribution, as are the distributions of the GLRT statistics in multivariate analysis of variance (MANOVA) procedures. In the high dimensional setting, i.e. when the size of the vectors grows at the same rate as the number of samples, a closed form expression is obtained for the asymptotic distribution of the GLRT statistics. This is, to our knowledge, the first exact characterization for the GLRT-based improperness testing.

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“…More generally, recent works [18]- [21] have shown that Stokes parameters provide a natural reparameterization for the second-order properties of bivariate signals. As a result, QNMF defines a new low-rank approximation tool for arbitrary bivariate signals, such as current velocities in oceanography [22] or polarized gravitational waves [23].…”

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confidence: 99%

Quaternion Non-Negative Matrix Factorization: Definition, Uniqueness, and Algorithm

Flamant

Miron

Brie

2020

IEEE Trans. Signal Process.

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This article introduces quaternion non-negative matrix factorization (QNMF), which generalizes the usual nonnegative matrix factorization (NMF) to the case of polarized signals. Polarization information is represented by Stokes parameters, a set of 4 energetic parameters widely used in polarimetric imaging. QNMF relies on two key ingredients: (i) the algebraic representation of Stokes parameters thanks to quaternions and (ii) the exploitation of physical constraints on Stokes parameters. These constraints generalize non-negativity to the case of polarized signals, encoding positive semi-definiteness of the covariance matrix associated which each source. Uniqueness conditions for QNMF are presented. Remarkably, they encompass known sufficient uniqueness conditions from NMF. Meanwhile, QNMF further relaxes NMF uniqueness conditions requiring sources to exhibit a certain zero-pattern, by leveraging the complete polarization information. We introduce a simple yet efficient algorithm called quaternion alternating least squares (QALS) to solve the QNMF problem in practice. Closed-form quaternion updates are obtained using the recently introduced generalized HR calculus. Numerical experiments on synthetic data demonstrate the relevance of the approach. QNMF defines a promising generic low-rank approximation tool to handle polarization, notably for blind source separation problems arising in imaging applications.

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Non-parametric characterization of gravitational-wave polarizations

Cited by 4 publications

References 9 publications

Polarized Signal Singular Spectrum Analysis with Complex SSA

Polarized Signal Singular Spectrum Analysis with Complex SSA

Exact Distribution and High-dimensional Asymptotics for Improperness Test of Complex Signals

Quaternion Non-Negative Matrix Factorization: Definition, Uniqueness, and Algorithm

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