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LearningImageSuperresol - Example-based Learning for...

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Example-based Learning for Single-Image Super-resolution Kwang In Kim 1 and Younghee Kwon 2 1 Max-Planck-Institute f¨ur biologische Kybernetik, Spemannstr. 38, D-72076 T¨ubingen, Germany 2 Korea Advanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-Ku, Taejon, Korea Abstract. This paper proposes a regression-based method for single- image super-resolution. Kernel ridge regression (KRR) is used to esti- mate the high-frequency details of the underlying high-resolution image. A sparse solution of KRR is found by combining the ideas of kernel matching pursuit and gradient descent, which allows time-complexity to be kept to a moderate level. To resolve the problem of ringing artifacts occurring due to the regularization effect, the regression results are post- processed using a prior model of a generic image class. Experimental results demonstrate the effectiveness of the proposed method. 1 Introduction Single-image super-resolution refers to the task of constructing a high-resolution enlargement of a given low-resolution image. This problem is inherently ill-posed as there are generally multiple high-resolution images that can produce the same low-resolution image. Accordingly, prior information is required to approach this problem. Often, this prior information is available either in the explicit form of an energy functional defined on the image class [9, 10], or in the implicit form of example images leading to example-based super-resolution [1–3, 5]. Previous example-based super-resolution algorithms can be characterized as nearest neighbor (NN)-based estimations [1–3] : during the training phase , pairs of low-resolution and the corresponding high-resolution image patches (sub-windows of images) are collected. Then, in the super-resolution phase , each patch of the given low-resolution image is compared to the stored low- resolution patches, and the high-resolution patch corresponding to the nearest low-resolution patch is selected as the output. For instance, Freeman et al. [2] posed the image super-resolution as the problem of estimating missing high- frequency details by interpolating the input low-resolution image into the de- sired scale (which results in a blurred image). Then, the super-resolution was performed by the NN-based estimation of high-frequency patches based on the corresponding patches of input low-frequency image. Although this method (and also other NN-based methods) has already shown an impressive performance, there is still room for improvement if one views the
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2 image super-resolution as a regression problem, i.e., finding a map f from the space of low-resolution image patches X to the space of target high-resolution patches Y . It is well known in the machine learning community that NN-based estimation suffers from overfitting where one obtains a function which explains the training data perfectly yet cannot be generalized to unknown data. In the super-resolution, this can result in noisy reconstructions at complex image re- gions (cf. Sect. 3). Accordingly, it is reasonable to expect that NN-based methods
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