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arXiv · 1605.07985

Compressed sensing for real measurements of quaternion signals

Agnieszka Badenska·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 real linear measurements, provided the 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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Agnieszka Badenska, Łukasz Błaszczyk. 2016-05-25. Compressed sensing for real measurements of quaternion signals. https://arxiv.org/abs/1605.07985

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