  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.
