The Mueller matrix cone and its application to filtering

The Mueller matrix cone and its application to filtering

We show that there is an isometry between the real ambient space of all Mueller matrices and the space of all Hermitian matrices which maps the Mueller matrices onto the positive semidefinite matrices. We use this to establish an optimality result for the filtering of Mueller matrices, which roughly...

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Veröffentlicht in:arXiv.org 2019-11
Hauptverfasser: Zander, Tim, Beyerer, Jürgen
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Correlation analysis
Eigenvalues
Filtration
Mathematical analysis
Matrix methods
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description We show that there is an isometry between the real ambient space of all Mueller matrices and the space of all Hermitian matrices which maps the Mueller matrices onto the positive semidefinite matrices. We use this to establish an optimality result for the filtering of Mueller matrices, which roughly says that it is always enough to filter the eigenvalues of the corresponding "coherency matrix". Then we further explain how the knowledge of the cone of Hermitian positive semidefinite matrices can be transferred to the cone of Mueller matrices with a special emphasis towards optimisation. In particular, we suggest that means of Mueller matrices should be computed within the corresponding Riemannian geometry.
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subjects Correlation analysis
Eigenvalues
Filtration
Mathematical analysis
Matrix methods
title The Mueller matrix cone and its application to filtering
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