Running high-resolution physical models is computationally expensive and essential for many disciplines. Agriculture, transportation, and energy are sectors that depend on high-resolution weather models, which typically consume many hours of large High Performance Computing (HPC) systems to deliver timely results. Many users cannot afford to run the desired resolution and are forced to use low resolution output. One simple solution is to interpolate results for visualization. It is also possible to combine an ensemble of low resolution models to obtain a better prediction. However, these approaches fail to capture the redundant information and patterns in the low-resolution input that could help improve the quality of prediction. In this paper, we propose and evaluate a strategy based on a deep neural network to learn a high-resolution representation from low-resolution predictions using weather forecast as a practical use case. We take a supervised learning approach, since obtaining labeled data can be done automatically. Our results show significant improvement when compared with standard practices and the strategy is still lightweight enough to run on modest computer systems.
A typical assumption of super-resolution techniques is that @math images with different perspectives are used to recover the high-resolution input. A common model is linear and takes the form where @math is the @math th image generated from the high-resolution input @math , @math translates and rotates the input, @math is a blur matrix, @math is a subsampling matrix, and @math is an additive noise. In this model, not only is @math unknown, but @math , @math and @math must be estimated as well. Non-linear models have also been explored, as in the work by He @cite_12 .
@cite_12
2523714292 2963470893 2755233754 2140257560
Despite the breakthroughs in accuracy and speed of single image super-resolution using faster and deeper convolutional neural networks, one central problem remains largely unsolved: how do we recover the finer texture details when we super-resolve at large upscaling factors? The behavior of optimization-based super-resolution methods is principally driven by the choice of the objective function. Recent work has largely focused on minimizing the mean squared reconstruction error. The resulting estimates have high peak signal-to-noise ratios, but they are often lacking high-frequency details and are perceptually unsatisfying in the sense that they fail to match the fidelity expected at the higher resolution. In this paper, we present SRGAN, a generative adversarial network (GAN) for image super-resolution (SR). To our knowledge, it is the first framework capable of inferring photo-realistic natural images for 4x upscaling factors. To achieve this, we propose a perceptual loss function which consists of an adversarial loss and a content loss. The adversarial loss pushes our solution to the natural image manifold using a discriminator network that is trained to differentiate between the super-resolved images and original photo-realistic images. In addition, we use a content loss motivated by perceptual similarity instead of similarity in pixel space. Our deep residual network is able to recover photo-realistic textures from heavily downsampled images on public benchmarks. An extensive mean-opinion-score (MOS) test shows hugely significant gains in perceptual quality using SRGAN. The MOS scores obtained with SRGAN are closer to those of the original high-resolution images than to those obtained with any state-of-the-art method. Despite the breakthroughs in accuracy and speed of single image super-resolution using faster and deeper convolutional neural networks, one central problem remains largely unsolved: how do we recover the finer texture details when we super-resolve at large upscaling factors? The behavior of optimization-based super-resolution methods is principally driven by the choice of the objective function. Recent work has largely focused on minimizing the mean squared reconstruction error. The resulting estimates have high peak signal-to-noise ratios, but they are often lacking high-frequency details and are perceptually unsatisfying in the sense that they fail to match the fidelity expected at the higher resolution. In this paper, we present SRGAN, a generative adversarial network (GAN) for image super-resolution (SR). To our knowledge, it is the first framework capable of inferring photo-realistic natural images for 4x upscaling factors. To achieve this, we propose a perceptual loss function which consists of an adversarial loss and a content loss. The adversarial loss pushes our solution to the natural image manifold using a discriminator network that is trained to differentiate between the super-resolved images and original photo-realistic images. In addition, we use a content loss motivated by perceptual similarity instead of similarity in pixel space. Our deep residual network is able to recover photo-realistic textures from heavily downsampled images on public benchmarks. An extensive mean-opinion-score (MOS) test shows hugely significant gains in perceptual quality using SRGAN. The MOS scores obtained with SRGAN are closer to those of the original high-resolution images than to those obtained with any state-of-the-art method. Super-resolution refers to the process of recovering the locations and amplitudes of a collection of point sources, represented as a discrete measure, given @math of its noisy low-frequency Fourier coefficients. The recovery process is highly sensitive to noise whenever the distance @math between the two closest point sources is less than @math . This paper studies the fundamental difficulty of super-resolution and the performance guarantees of a subspace method called MUSIC in the regime that @math . The most important quantity in our theory is the minimum singular value of the Vandermonde matrix whose nodes are specified by the source locations. Under the assumption that the nodes are closely spaced within several well-separated clumps, we derive a sharp and non-asymptotic lower bound for this quantity. Our estimate is given as a weighted @math sum, where each term only depends on the configuration of each individual clump. This implies that, as the noise increases, the super-resolution capability of MUSIC degrades according to a power law where the exponent depends on the cardinality of the largest clump. Numerical experiments validate our theoretical bounds for the minimum singular value and the resolution limit of MUSIC. When there are @math point sources located on a grid with spacing @math , the fundamental difficulty of super-resolution can be quantitatively characterized by a min-max error, which is the reconstruction error incurred by the best possible algorithm in the worst-case scenario. We show that the min-max error is closely related to the minimum singular value of Vandermonde matrices, and we provide a non-asymptotic and sharp estimate for the min-max error, where the dominant term is @math . Nearly all super-resolution algorithms are based on the fundamental constraints that the super-resolution image should generate low resolution input images when appropriately warped and down-sampled to model the image formation process. (These reconstruction constraints are normally combined with some form of smoothness prior to regularize their solution.) We derive a sequence of analytical results which show that the reconstruction constraints provide less and less useful information as the magnification factor increases. We also validate these results empirically and show that, for large enough magnification factors, any smoothness prior leads to overly smooth results with very little high-frequency content. Next, we propose a super-resolution algorithm that uses a different kind of constraint in addition to the reconstruction constraints. The algorithm attempts to recognize local features in the low-resolution images and then enhances their resolution in an appropriate manner. We call such a super-resolution algorithm a hallucination or reconstruction algorithm. We tried our hallucination algorithm on two different data sets, frontal images of faces and printed Roman text. We obtained significantly better results than existing reconstruction-based algorithms, both qualitatively and in terms of RMS pixel error.