L1-norm minimization for quaternion signals
  The l1-norm minimization problem plays an important role in the compressed sensing (CS) theory. We present in this letter an algorithm for solving the problem of l1-norm minimization for quaternion signals by converting it to second-order cone programming. An application example of the proposed algorithm is also given for practical guidelines of perfect recovery of quaternion signals. The proposed algorithm may find its potential application when CS theory meets the quaternion signal processing. 
Jiasong Wu, Xu Zhang, Xiaoqing Wang, Lotfi Senhadji, Huazhong Shu
cs.NA cs.DS cs.IT math.IT