A higher order model for image restoration: the one-dimensional case

The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [SIAM J. Sci. Comput., 22 (2000), pp. 503–516] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed, and it is proved analytically that the higher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.