Abstract: A novel variational denoising model is obtained by replacing the (1,3)H^-1(1,3)-norm by norms of wavelet coefficients in the OSV model. The associated Euler-Lagrange equation leads to a nonlinear partial differential equation of second order in the wavelet domain. And we also prove the existence theorem of minimizer for the new model by means of Poincare’s inequality and the lower semi-continuity of bounded variation functions. Numerical experiments show that the proposed model not only improves the denoising performance significantly, but also can preserve the appealing visual quality of images.

Key words: total variation, wavelet, image denoising, Euler-Lagrange equation, minimizer of energy functional