四元数信号实测量的压缩感知
Compressed sensing for real measurements of quaternion signals
摘要：
本文研究了四元数代数中的压缩感知方法。我们证明，它是可能的唯一重建-由$\ell_1$范数最小化-稀疏四元数信号从有限数量的实际线性测量，提供的测量矩阵满足所谓的限制等距属性与足够小的常数。我们还提供了误差估计的重建的非稀疏四元数信号在噪声和无噪声的情况下。
英文摘要：
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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