# A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration

@article{Chan1999ANP, title={A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration}, author={Tony F. Chan and Gene H. Golub and Pep Mulet}, journal={SIAM J. Sci. Comput.}, year={1999}, volume={20}, pages={1964-1977} }

We present a new method for solving total variation (TV) minimization problems in image restoration. The main idea is to remove some of the singularity caused by the nondifferentiability of the quantity $|\nabla u|$ in the definition of the TV-norm before we apply a linearization technique such as Newton's method. This is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function, which can be interpreted as the normal vector to…

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