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arXiv · 1704.08202

Compressed sensing in the quaternion algebra

Agnieszka Badeńska·Łukasz Błaszczyk
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Abstract

The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$-norm minimization - a sparse quaternion signal from a limited number of its linear measurements, provided the quaternion measurement matrix satisfies so-called restricted isometry property with a sufficiently small constant. We also provide error estimates for the reconstruction of a non-sparse quaternion signal in the noisy and noiseless cases.

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BibTeXRIS

Agnieszka Badeńska, Łukasz Błaszczyk. 2017-04-25. Compressed sensing in the quaternion algebra. https://arxiv.org/abs/1704.08202

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