Compressed sensing in the quaternion algebra

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.

15 pages, 2 figures. arXiv admin note: text overlap with arXiv:1605.07985