Image Smoothing via Truncated Total Variation

We present a new regularizer for image smoothing which is particularly effective for diminishing insignificant details, while preserving salient edges. The proposed regularizer relates in spirit to total variation which penalizes all the gradients, while our method just penalizes part of the gradients and leaves the significant edges unchanged. Though the proposed regularizer is a piecewise function, which is hard to optimize, we can unify it to a mathematically sound penalty. The unified penalty term is easy to optimize using recent fast solvers and hard thresholding operation. We show some potential applications of the proposed regularizer, including texture removal and compression artifact restoration. The results show the efficiency of the proposed regularizer.