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原文：
Blind Super-Resolution Kernel Estimation using an Internal-GAN
Sefi Bell-Kligler Assaf Shocher Michal Irani
Dept. of Computer Science and Applied Math The Weizmann Institute of Science, Israel
Abstract
Super resolution (SR) methods typically assume that the low-resolution (LR) image was downscaled from the unknown high-resolution (HR) image by a fixed lsquo;idealrsquo; downscaling kernel (e.g. Bicubic downscaling). However, this is rarely the case in real LR images, in contrast to synthetically generated SR datasets. When the assumed downscaling kernel deviates from the true one, the performance of SR methods significantly deteriorates. This gave rise to Blind-SR – namely, SR when the downscaling kernel (“SR-kernel”) is unknown. It was further shown that the true SR-kernel is the one that maximizes the recurrence of patches across scales of the LR image. In this paper we show how this powerful cross-scale recurrence property can be realized using Deep Internal Learning. We introduce “KernelGAN”, an image-specific Internal-GAN [29], which trains solely on the LR test image at test time, and learns its internal distribution of patches. Its Generator is trained to produce a downscaled version of the LR test image, such that its Discriminator cannot distinguish between the patch distribution of the downscaled image, and the patch distribution of the original LR image. The Generator, once trained, constitutes the downscaling operation with the correct image-specific SR-kernel. KernelGAN is fully unsupervised, requires no training data other than the input image itself, and leads to state-of-the-art results in Blind-SR when plugged into existing SR algorithms. 1
Introduction
The basic model of SR assumes that the low-resolution input image ILR is the result of down-scaling a high-resolution image IHR by a scaling factor s using some kernel ks (the 'SR kernel'), namely:
ILR = (IHR lowast; ks) darr;s (1)
The goal is to recover IHR given ILR. This problem is ill-posed even when the SR-Kernel is assumed known (an assumption made by most SR methods – older [8, 32, 7] and more recent [5, 20, 19, 21, 38, 35, 12]). A boost in SR performance was achieved in the past few years introducing Deep-Learning based methods [5, 20, 19, 21, 38, 35, 12]. However, since most SR methods train on synthetically downscaled images, they implicitly rely on the SR-kernel ks being fixed and lsquo;idealrsquo; (usually a Bicubic downscaling kernel with antialiasing– MATLABrsquo;s default imresize command). Real LR images, however, rarely obey this assumption. This results in poor SR performance by state-of-the-art (SotA) methods when applied to real or lsquo;non-idealrsquo; LR images (see Fig. 1a).
The SR kernel of real LR images is influenced by the sensor optics as well as by tiny camera motion of the hand-held camera, resulting in a different non-ideal SR-kernel for each LR image, even if taken by the same sensor. It was shown in [26] that the effect of using an incorrect SR-kernel is of greater influence on the SR performance than any choice of an image prior. This observation was later shown
1Project funded by the European Research Council (ERC) under the Horizon 2020 research amp; innovation program (grant No. 788535)
Comparison to SotA SR methods (SR 4):
times;
Since they train on rsquo;idealrsquo; LR images, they perform poorly on real non-ideal LR images.
Bicubic EDSR RCAN KernelGAN(Ours) Ground
LR Input image interpolation [21] [38] SR method: [30] Truth HR
Comparison to SotA Blind-SR methods (SRtimes;4):
PDN WDSR Kernel of [24] KernelGAN(Ours) Ground
LR Input image [34] [36] SR method:[30] SR method:[30] Truth HR
Figure 1: SR 4 on real lsquo;non-idealrsquo; LR images (downloaded from the internet, or downscaled by an unknown kernel). Full images and additional examples in supplementary material (please zoom in on screen).
times;
to hold also for deep-learning based priors [30]. The importance of the SR-kernel accuracy was further analyzed empirically in [27].
The problem of SR with an unknown kernel is known as Blind SR. Some Blind-SR methods [33, 17, 14, 13, 3] were
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