Abstract Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularizer 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.