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Unformatted text preview: Image Super-Resolution using Gradient Profile Prior Jian Sun 1 Jian Sun 2 Zongben Xu 1 Heung-Yeung Shum 2 1 Xi’an Jiaotong University 2 Microsoft Research Asia Xi’an, P. R. China Beijing, P. R. China Abstract In this paper, we propose an image super-resolution ap- proach using a novel generic image prior – gradient profile prior, which is a parametric prior describing the shape and the sharpness of the image gradients. Using the gradient profile prior learned from a large number of natural im- ages, we can provide a constraint on image gradients when we estimate a hi-resolution image from a low-resolution im- age. With this simple but very effective prior, we are able to produce state-of-the-art results. The reconstructed hi- resolution image is sharp while has rare ringing or jaggy artifacts. 1. Introduction The goal of single image super-resolution is to estimate a hi-resolution (HR) image from a low-resolution (LR) in- put. There are mainly three categories of approach for this problem: interpolation based methods, reconstruction based methods, and learning based methods. The interpolation based methods [ 12 , 29 , 18 ] are simple but tend to blur the high frequency details. The reconstruction based methods [ 14 , 2 , 19 , 3 ] enforce a reconstruction constraint which re- quires that the smoothed and down-sampled version of the HR image should be close to the LR image. The learning based methods [ 10 , 9 , 26 , 5 , 28 , 2 , 7 , 20 , 31 ] “hallucinate” high frequency details from a training set of HR/LR im- age pairs. The learning based approach highly relies on the similarity between the training set and the test set. It is still unclear how many training examples are sufficient for the generic images. To design a good image super-resolution algorithm, the essential issue is how to apply a good prior or constraint on the HR image because of the ill-posedness of the im- age super-resolution. Generic smoothness prior [ 25 , 11 ] and edge smoothness prior [ 21 , 1 , 6 , 7 , 22 , 27 ] are two widely used priors. In this paper, we propose a novel generic image prior — gradient profile prior for the gradient field of the natural im- p ( x ) x 1 x 2 x p ( x ) x 1 x 2 x (a) (b) (c) Figure 1. Gradient profile. (a) two edges with different sharp- ness. (b) gradient maps (normalized and inverted magnitude) of two rectangular regions in (a). p ( x ) is a gradient profile pass- ing through the edge pixel (zero crossing pixel) x , by tracing along gradient directions (two sides) pixel by pixel until the gra- dient magnitude does not decrease at x 1 and x 2 . (c) 1D curves of two gradient profiles. age. The gradient profile is a 1-D profile along the gradient direction of the zero-crossing pixel in the image. The gra- dient profile prior is a parametric distribution describing the shape and the sharpness of the gradient profiles in natural image. One of our observations is that the shape statistics of the gradient profiles in natural image is quit stable and...
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- Spring '10