A Zero-attracting Quaternion-valued Least Mean Square Algorithm for   Sparse System Identification
  Recently, quaternion-valued signal processing has received more and more attention. In this paper, the quaternion-valued sparse system identification problem is studied for the first time and a zero-attracting quaternion-valued least mean square (LMS) algorithm is derived by considering the $l_1$ norm of the quaternion-valued adaptive weight vector. By incorporating the sparsity information of the system into the update process, a faster convergence speed is achieved, as verified by simulation results. 
Mengdi Jiang, Wei Liu, Yi Li
math.NA math.CV math.OC