One Dimensional Fractional Order Tgv : Gamma-convergence and Bilevel Training Scheme
نویسندگان
چکیده
New fractional r -order seminorms, TGV r , r ∈ R , r ≥ 1 , are proposed in the one-dimensional (1D) setting, as a generalization of the integer order TGV k seminorms, k ∈ N . The fractional r -order TGV r -seminorms are shown to be intermediate between the integer order TGV k -seminorms. A bilevel training scheme is proposed, where under a box constraint a simultaneous optimization with respect to parameters and order of derivation is performed. Existence of solutions to the bilevel training scheme is proved by Γ–convergence. Finally, the numerical landscape of the cost function associated to the bilevel training scheme is discussed for two numerical examples.
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