  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.
