Publication 12-CNA-008
** A Note on Variational Models for Denoising**

Rustum Choksi

Department of Mathematics and Statistics

McGill University, Montreal, Canada

rchoksi@math.mcgill.ca

Irene Fonseca

Department of Mathematical Sciences

Carnegie Mellon University

Pittsburgh, PA 15213

fonseca@andrew.cmu.edu

Barbara Zwicknagl

Department of Mathematical Sciences

Carnegie Mellon University

Pittsburgh, PA 15213

bzwick@andrew.cmu.edu

**Abstract:** A class of variational models for image and signal denoising is considered. These models are based on the minimization of energy functionals consisting of a fidelity term together with higher-order regularization. In addition to the choices of function spaces to measure fidelity and impose regularization, different scaling exponents appear. The relationship between certain desirable properties for these models and the choice of function spaces and scaling exponents is addressed. In particular, stability of these models is discussed with respect to deterministic noise perturbations, captured via oscillatory sequences converging weakly to zero.

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