We consider image transformation problems, where an input image is transformed into an output image. Recent methods for such problems typically train feed-forward convolutional neural networks using a loss between the output and ground-truth images. Parallel work has shown that high-quality images can be generated by defining and optimizing loss functions based on high-level features extracted from pretrained networks. We combine the benefits of both approaches, and propose the use of perceptual loss functions for training feed-forward networks for image transformation tasks. We show results on image style transfer, where a feed-forward network is trained to solve the optimization problem proposed by in real-time. Compared to the optimization-based method, our network gives similar qualitative results but is three orders of magnitude faster. We also experiment with single-image super-resolution, where replacing a per-pixel loss with a perceptual loss gives visually pleasing results.
@cite_35: 
@cite_41: 
@cite_36: 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 methods. We further show how this combined approach can be applied to obtain super resolution from as little as a single image (with no database or prior examples). Our approach is based on the observation that patches in a natural image tend to redundantly recur many times inside the image, both within the same scale, as well as across different scales. Recurrence of patches within the same image scale (at subpixel misalignments) gives rise to the classical super-resolution, whereas recurrence of patches across different 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.
@cite_29: 
@cite_2: A thorough investigation of the application of support vector regression (SVR) to the superresolution problem is conducted through various frameworks. Prior to the study, the SVR problem is enhanced by finding the optimal kernel. This is done by formulating the kernel learning problem in SVR form as a convex optimization problem, specifically a semi-definite programming (SDP) problem. An additional constraint is added to reduce the SDP to a quadratically constrained quadratic programming (QCQP) problem. After this optimization, investigation of the relevancy of SVR to superresolution proceeds with the possibility of using a single and general support vector regression for all image content, and the results are impressive for small training sets. This idea is improved upon by observing structural properties in the discrete cosine transform (DCT) domain to aid in learning the regression. Further improvement involves a combination of classification and SVR-based techniques, extending works in resolution synthesis. This method, termed kernel resolution synthesis, uses specific regressors for isolated image content to describe the domain through a partitioned look of the vector space, thereby yielding good results
@cite_4: This paper proposes a framework for single-image super-resolution. The underlying idea is to learn a map from input low-resolution images to target high-resolution images based on example pairs of input and output images. Kernel ridge regression (KRR) is adopted for this purpose. To reduce the time complexity of training and testing for KRR, a sparse solution is found by combining the ideas of kernel matching pursuit and gradient descent. As a regularized solution, KRR leads to a better generalization than simply storing the examples as has been done in existing example-based algorithms and results in much less noisy images. However, this may introduce blurring and ringing artifacts around major edges as sharp changes are penalized severely. A prior model of a generic image class which takes into account the discontinuity property of images is adopted to resolve this problem. Comparison with existing algorithms shows the effectiveness of the proposed method.
@cite_8: We propose a fast regression model for practical single image super-resolution based on in-place examples, by leveraging two fundamental super-resolution approaches- learning from an external database and learning from self-examples. Our in-place self-similarity refines the recently proposed local self-similarity by proving that a patch in the upper scale image have good matches around its origin location in the lower scale image. Based on the in-place examples, a first-order approximation of the nonlinear mapping function from low-to high-resolution image patches is learned. Extensive experiments on benchmark and real-world images demonstrate that our algorithm can produce natural-looking results with sharp edges and preserved fine details, while the current state-of-the-art algorithms are prone to visual artifacts. Furthermore, our model can easily extend to deal with noise by combining the regression results on multiple in-place examples for robust estimation. The algorithm runs fast and is particularly useful for practical applications, where the input images typically contain diverse textures and they are potentially contaminated by noise or compression artifacts.
@cite_48: This paper addresses the problem of generating a super-resolution (SR) image from a single low-resolution input image. We approach this problem from the perspective of compressed sensing. The low-resolution image is viewed as downsampled version of a high-resolution image, whose patches are assumed to have a sparse representation with respect to an over-complete dictionary of prototype signal-atoms. The principle of compressed sensing ensures that under mild conditions, the sparse representation can be correctly recovered from the downsampled signal. We will demonstrate the effectiveness of sparsity as a prior for regularizing the otherwise ill-posed super-resolution problem. We further show that a small set of randomly chosen raw patches from training images of similar statistical nature to the input image generally serve as a good dictionary, in the sense that the computed representation is sparse and the recovered high-resolution image is competitive or even superior in quality to images produced by other SR methods.
@cite_52: 
@cite_46: The aim of single image super-resolution is to reconstruct a high-resolution image from a single low-resolution input. Although the task is ill-posed it can be seen as finding a non-linear mapping from a low to high-dimensional space. Recent methods that rely on both neighborhood embedding and sparse-coding have led to tremendous quality improvements. Yet, many of the previous approaches are hard to apply in practice because they are either too slow or demand tedious parameter tweaks. In this paper, we propose to directly map from low to high-resolution patches using random forests. We show the close relation of previous work on single image super-resolution to locally linear regression and demonstrate how random forests nicely fit into this framework. During training the trees, we optimize a novel and effective regularized objective that not only operates on the output space but also on the input space, which especially suits the regression task. During inference, our method comprises the same well-known computational efficiency that has made random forests popular for many computer vision problems. In the experimental part, we demonstrate on standard benchmarks for single image super-resolution that our approach yields highly accurate state-of-the-art results, while being fast in both training and evaluation.
@cite_28: We address the problem of image upscaling in the form of single image super-resolution based on a dictionary of low- and high-resolution exemplars. Two recently proposed methods, Anchored Neighborhood Regression (ANR) and Simple Functions (SF), provide state-of-the-art quality performance. Moreover, ANR is among the fastest known super-resolution methods. ANR learns sparse dictionaries and regressors anchored to the dictionary atoms. SF relies on clusters and corresponding learned functions. We propose A+, an improved variant of ANR, which combines the best qualities of ANR and SF. A+ builds on the features and anchored regressors from ANR but instead of learning the regressors on the dictionary it uses the full training material, similar to SF. We validate our method on standard images and compare with state-of-the-art methods. We obtain improved quality (i.e. 0.2–0.7 dB PSNR better than ANR) and excellent time complexity, rendering A+ the most efficient dictionary-based super-resolution method to date.
@cite_32: We propose a Bayesian approach to image hallucination. Given a generic low resolution image, we hallucinate a high resolution image using a set of training images. Our work is inspired by recent progress on natural image statistics that the priors of image primitives can be well represented by examples. Specifically, primal sketch priors (e.g., edges, ridges and corners) are constructed and used to enhance the quality of the hallucinated high resolution image. Moreover, a contour smoothness constraint enforces consistency of primitives in the hallucinated image by a Markov-chain based inference algorithm. A reconstruction constraint is also applied to further improve the quality of the hallucinated image. Experiments demonstrate that our approach can hallucinate high quality super-resolution images.
@cite_19: 
@cite_27: This paper proposes a robust single-image super-resolution method for enlarging low quality web image video degraded by downsampling and compression. To simultaneously improve the resolution and perceptual quality of such web image video, we bring forward a practical solution which combines adaptive regularization and learning-based super-resolution. The contribution of this work is twofold. First, we propose to analyze the image energy change characteristics during the iterative regularization process, i.e., the energy change ratio between primitive (e.g., edges, ridges and corners) and nonprimitive fields. Based on the revealed convergence property of the energy change ratio, appropriate regularization strength can then be determined to well balance compression artifacts removal and primitive components preservation. Second, we verify that this adaptive regularization can steadily and greatly improve the pair matching accuracy in learning-based super-resolution. Consequently, their combination effectively eliminates the quantization noise and meanwhile faithfully compensates the missing high-frequency details, yielding robust super-resolution performance in the compression scenario. Experimental results demonstrate that our solution produces visually pleasing enlargements for various web images videos.
@cite_34: We propose a simple but effective upsampling method for automatically enhancing the image video resolution, while preserving the essential structural information. The main advantage of our method lies in a feedback-control framework which faithfully recovers the high-resolution image information from the input data, without imposing additional local structure constraints learned from other examples. This makes our method independent of the quality and number of the selected examples, which are issues typical of learning-based algorithms, while producing high-quality results without observable unsightly artifacts. Another advantage is that our method naturally extends to video upsampling, where the temporal coherence is maintained automatically. Finally, our method runs very fast. We demonstrate the effectiveness of our algorithm by experimenting with different image video data.
@cite_16: We propose a new high-quality and efficient single-image upscaling technique that extends existing example-based super-resolution frameworks. In our approach we do not rely on an external example database or use the whole input image as a source for example patches. Instead, we follow a local self-similarity assumption on natural images and extract patches from extremely localized regions in the input image. This allows us to reduce considerably the nearest-patch search time without compromising quality in most images. Tests, that we perform and report, show that the local self-similarity assumption holds better for small scaling factors where there are more example patches of greater relevance. We implement these small scalings using dedicated novel nondyadic filter banks, that we derive based on principles that model the upscaling process. Moreover, the new filters are nearly biorthogonal and hence produce high-resolution images that are highly consistent with the input image without solving implicit back-projection equations. The local and explicit nature of our algorithm makes it simple, efficient, and allows a trivial parallel implementation on a GPU. We demonstrate the new method ability to produce high-quality resolution enhancement, its application to video sequences with no algorithmic modification, and its efficiency to perform real-time enhancement of low-resolution video standard into recent high-definition formats.
@cite_25: This paper addresses the problem of learning over-complete dictionaries for the coupled feature spaces, where the learned dictionaries also reflect the relationship between the two spaces. A Bayesian method using a beta process prior is applied to learn the over-complete dictionaries. Compared to previous couple feature spaces dictionary learning algorithms, our algorithm not only provides dictionaries that customized to each feature space, but also adds more consistent and accurate mapping between the two feature spaces. This is due to the unique property of the beta process model that the sparse representation can be decomposed to values and dictionary atom indicators. The proposed algorithm is able to learn sparse representations that correspond to the same dictionary atoms with the same sparsity but different values in coupled feature spaces, thus bringing consistent and accurate mapping between coupled feature spaces. Another advantage of the proposed method is that the number of dictionary atoms and their relative importance may be inferred non-parametrically. We compare the proposed approach to several state-of-the-art dictionary learning methods by applying this method to single image super-resolution. The experimental results show that dictionaries learned by our method produces the best super-resolution results compared to other state-of-the-art methods.
@cite_12: Self-similarity based super-resolution (SR) algorithms are able to produce visually pleasing results without extensive training on external databases. Such algorithms exploit the statistical prior that patches in a natural image tend to recur within and across scales of the same image. However, the internal dictionary obtained from the given image may not always be sufficiently expressive to cover the textural appearance variations in the scene. In this paper, we extend self-similarity based SR to overcome this drawback. We expand the internal patch search space by allowing geometric variations. We do so by explicitly localizing planes in the scene and using the detected perspective geometry to guide the patch search process. We also incorporate additional affine transformations to accommodate local shape variations. We propose a compositional model to simultaneously handle both types of transformations. We extensively evaluate the performance in both urban and natural scenes. Even without using any external training databases, we achieve significantly superior results on urban scenes, while maintaining comparable performance on natural scenes as other state-of-the-art SR algorithms.
@cite_1: We propose a deep learning method for single image super-resolution (SR). Our method directly learns an end-to-end mapping between the low high-resolution images. The mapping is represented as a deep convolutional neural network (CNN) that takes the low-resolution image as the input and outputs the high-resolution one. We further show that traditional sparse-coding-based SR methods can also be viewed as a deep convolutional network. But unlike traditional methods that handle each component separately, our method jointly optimizes all layers. Our deep CNN has a lightweight structure, yet demonstrates state-of-the-art restoration quality, and achieves fast speed for practical on-line usage. We explore different network structures and parameter settings to achieve trade-offs between performance and speed. Moreover, we extend our network to cope with three color channels simultaneously, and show better overall reconstruction quality.
@cite_0: This paper presents a new approach to single-image superresolution, based upon sparse signal representation. Research on image statistics suggests that image patches can be well-represented as a sparse linear combination of elements from an appropriately chosen over-complete dictionary. Inspired by this observation, we seek a sparse representation for each patch of the low-resolution input, and then use the coefficients of this representation to generate the high-resolution output. Theoretical results from compressed sensing suggest that under mild conditions, the sparse representation can be correctly recovered from the downsampled signals. By jointly training two dictionaries for the low- and high-resolution image patches, we can enforce the similarity of sparse representations between the low-resolution and high-resolution image patch pair with respect to their own dictionaries. Therefore, the sparse representation of a low-resolution image patch can be applied with the high-resolution image patch dictionary to generate a high-resolution image patch. The learned dictionary pair is a more compact representation of the patch pairs, compared to previous approaches, which simply sample a large amount of image patch pairs , reducing the computational cost substantially. The effectiveness of such a sparsity prior is demonstrated for both general image super-resolution (SR) and the special case of face hallucination. In both cases, our algorithm generates high-resolution images that are competitive or even superior in quality to images produced by other similar SR methods. In addition, the local sparse modeling of our approach is naturally robust to noise, and therefore the proposed algorithm can handle SR with noisy inputs in a more unified framework.
Image super-resolution is a classic problem for which a wide variety of techniques have been developed. Yang al @cite_41 provide an exhaustive evaluation of the prevailing techniques prior to the widespread adoption of convolutional neural networks. They group super-resolution techniques into prediction-based methods (bilinear, bicubic, Lanczos, @cite_35 ), edge-based methods @cite_16 @cite_52 , statistical methods @cite_34 @cite_4 @cite_27 , patch-based methods @cite_16 @cite_19 @cite_29 @cite_36 @cite_8 @cite_32 @cite_2 @cite_25 , and sparse dictionary methods @cite_48 @cite_0 . Recently @cite_1 achieved excellent performance on single-image super-resolution using a three-layer convolutional neural network trained with a per-pixel Euclidean loss. Other recent state-of-the-art methods include @cite_28 @cite_46 @cite_12 .