On convergent finite difference schemes for variational-PDE-based image processing

We study an adaptive anisotropic Huber functional-based image restoration scheme. Using a combination of L2-L1 regularization functions, an adaptive Huber functional-based energy minimization model provides denoising with edge preservation in noisy digital images. We study a convergent finite difference scheme based on continuous piecewise linear functions and use a variable splitting scheme, namely the Split Bregman (In: Goldstein and Osher, SIAM J Imaging Sci 2(2):323-343, 2009) algorithm, to obtain the discrete minimizer. Experimental results are given in image denoising and comparison with additive operator splitting, dual fixed point, and projected gradient schemes illustrates that the best convergence rates are obtained for our algorithm.