  The main goal of this paper is to propose a new quaternion total variation
regularization model for solving linear ill-posed quaternion inverse problems,
which arise from three-dimensional signal filtering or color image processing.
The quaternion total variation term in the model is represented by
collaborative total variation regularization and approximated by a quaternion
iteratively reweighted norm. A novel flexible quaternion generalized minimal
residual method is presented to quickly solve this model. An improved
convergence theory is established to obtain a sharp upper bound of the residual
norm of quaternion minimal residual method (QGMRES). The convergence theory is
also presented for preconditioned QGMRES. Numerical experiments indicate the
superiority of the proposed model and algorithms over the state-of-the-art
methods in terms of iteration steps, CPU time, and the quality criteria of
restored color images.
