  Owing to the edge preserving ability and low computational cost of the total
variation (TV), variational models with the TV regularization have been widely
investigated in the field of multiplicative noise removal. The key points of
the successful application of these models lie in: the optimal selection of the
regularization parameter which balances the data-fidelity term with the TV
regularizer; the efficient algorithm to compute the solution. In this paper, we
propose two fast algorithms based on the linearized technique, which are able
to estimate the regularization parameter and recover the image simultaneously.
In the iteration step of the proposed algorithms, the regularization parameter
is adjusted by a special discrepancy function defined for multiplicative noise.
The convergence properties of the proposed algorithms are proved under certain
conditions, and numerical experiments demonstrate that the proposed algorithms
overall outperform some state-of-the-art methods in the PSNR values and
computational time.
