Communications in Mathematical Sciences
Volume 12 (2014)
A few remarks on variational models for denoising
Pages: 843 – 857
Variational models for image and signal denoising 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. In this note we present a few simple remarks on (i) the stability with respect to deterministic noise perturbations, captured via oscillatory sequences converging weakly to zero, and (ii) exact reconstruction.
denoising, higher-order regularization, stability, weak convergence, Brezis-Lieb condition
2010 Mathematics Subject Classification