Single Image Super-resolution With Detail Enhancement Based on Local Fractal Analysis of Gradient

In this paper, we propose a single image super-resolution and enhancement algorithm using local fractal analysis. If we treat the pixels of a natural image as a fractal set, the image gradient can then be regarded as a measure of the fractal set. According to the scale invariance (a special case of bi-Lipschitz invariance) feature of fractal dimension, we will be able to estimate the gradient of a high-resolution image from that of a low-resolution one. Moreover, the high-resolution image can be further enhanced by preserving the local fractal length of gradient during the up-sampling process. We show that a regularization term based on the scale invariance of fractal dimension and length can be effective in recovering details of the high-resolution image. Analysis is provided on the relation and difference among the proposed approach and some other state of the art interpolation methods. Experimental results show that the proposed method has superior super-resolution and enhancement results as compared to other competitors.