An adaptive norm algorithm for image restoration

We propose an adaptive norm strategy designed for the restora- tion of images contaminated by blur and noise. Standard Tikhonov regularization can give good results with Gaussian noise and smooth images, but can oversmooth the output. On the other hand, L1-TV (Total Variation) regularization has superior performance with some non-Gaussian noise and controls both size of jumps and geometry of object boundaries in the image but smooth parts of the recovered images can be blocky. According to a coherence map of the image (which detects smooth regions or edges), determined here by a threshold structure tensor, we apply L2-norm or L1-norm regularization to di®erent parts of the image. The solution of this general approach is obtained by a fast algorithm based on the half-quadratic technique recently proposed in [2] for L1-TV regularization. Some numerical results show the e®ectiveness of our adaptive norm image restoration strategy.