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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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