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single_image_SR - Super-Resolution from a Single Image...

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Super-Resolution from a Single Image Daniel Glasner Shai Bagon Michal Irani Dept. of Computer Science and Applied Mathematics The Weizmann Institute of Science Rehovot 76100, Israel Abstract Methods for super-resolution can be broadly classified into two families of methods: (i) The classical multi-image super-resolution (combining images obtained at subpixel misalignments), and (ii) Example-Based super-resolution (learning correspondence between low and high resolution image patches from a database). In this paper we propose a unified framework for combining these two families of meth- ods. We further show how this combined approach can be applied to obtain super resolution from as little as a sin- gle image (with no database or prior examples). Our ap- proach is based on the observation that patches in a natu- ral image tend to redundantly recur many times inside the image, both within the same scale, as well as across differ- ent scales. Recurrence of patches within the same image scale (at subpixel misalignments) gives rise to the classical super-resolution, whereas recurrence of patches across dif- ferent scales of the same image gives rise to example-based super-resolution. Our approach attempts to recover at each pixel its best possible resolution increase based on its patch redundancy within and across scales. 1. Introduction The goal of Super-Resolution ( SR ) methods is to recover a high resolution image from one or more low resolution input images. Methods for SR can be broadly classified into two families of methods: (i) The classical multi-image super-resolution, and (ii) Example-Based super-resolution. In the classical multi-image SR (e.g., [12, 5, 8] to name just a few) a set of low-resolution images of the same scene are taken (at subpixel misalignments). Each low resolution im- age imposes a set of linear constraints on the unknown high- resolution intensity values. If enough low-resolution im- ages are available (at subpixel shifts), then the set of equa- tions becomes determined and can be solved to recover the high-resolution image. Practically, however, this approach is numerically limited only to small increases in resolu- tion [3, 14] (by factors smaller than 2 ). These limitations have lead to the development of Input image I Various scales of I Figure 1: Patch recurrence within and across scales of a single image. Source patches in I are found in different loca- tions and in other image scales of I (solid-marked squares). The high-res corresponding parent patches (dashed-marked squares) provide an indication of what the (unknown) high-res parents of the source patches might look like. “Example-Based Super-Resolution” also termed “image hallucination” (introduced by [10, 11, 2] and extended later by others e.g. [13]). In example-based SR, correspon- dences between low and high resolution image patches are learned from a database of low and high resolution image pairs (usually with a relative scale factor of 2 ), and then applied to a new low-resolution image to recover its most likely high-resolution version. Higher SR factors have of-
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