Automated parameter selection in the $L^1\text{-}{L}^2$-TV model for removing Gaussian plus impulse noise

The minimization of a functional consisting of a combined L ¹/L ²-data-fidelity term and a total variation term, named L ¹-L ²-TV model, is considered to remove a mixture of Gaussian and impulse noise in images, which are possibly additionally deformed by some convolution operator. We investigate analytically the stability of this model with respect to its parameters and link it to a constrained minimization problem. Based on these investigations and a statistical characterization of the mixed Gaussian-impulse noise a fully automated parameter selection algorithm for the L ¹-L ²-TV model is presented. It is shown by numerical experiments that the proposed method finds parameters with which noise is removed considerably while features are preserved in images. (paper)