Graduated adaptive image denoising: local compromise between total variation and isotropic diffusion

We introduce variants of the variational image denoising method proposed by Blomgren et al. (In: Numerical Analysis 1999 (Dundee), pp. 43–67. Chapman & Hall, Boca Raton, FL, 2000), which interpolates between total-variation denoising and isotropic diffusion denoising. We study how parameter choices affect results and allow tuning between TV denoising and isotropic diffusion for respecting texture on one spatial scale while denoising features assumed to be noise on finer spatial scales. Furthermore, we prove existence and (where appropriate) uniqueness of minimizers. We consider both L2 and L1 data fidelity terms.