Author

# John Wright

Other affiliations: General Electric, Microsoft, Urbana University ...read more

Bio: John Wright is an academic researcher from Columbia University. The author has contributed to research in topics: Medicine & Sparse approximation. The author has an hindex of 56, co-authored 277 publications receiving 37903 citations. Previous affiliations of John Wright include General Electric & Microsoft.

Topics: Medicine, Sparse approximation, Proton, Matrix (mathematics), Physics

##### Papers published on a yearly basis

##### Papers

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TL;DR: This work considers the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise, and proposes a general classification algorithm for (image-based) object recognition based on a sparse representation computed by C1-minimization.

Abstract: We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.

9,658 citations

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TL;DR: In this paper, the authors prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the e1 norm.

Abstract: This article is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individuallyq We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the e1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces.

6,783 citations

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TL;DR: This paper presents a new approach to single-image superresolution, based upon sparse signal representation, which generates high-resolution images that are competitive or even superior in quality to images produced by other similar SR methods.

Abstract: 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.

4,958 citations

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29 Apr 2010

TL;DR: This review paper highlights a few representative examples of how the interaction between sparse signal representation and computer vision can enrich both fields, and raises a number of open questions for further study.

Abstract: Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on nontraditional applications where the goal is not just to obtain a compact high-fidelity representation of the observed signal, but also to extract semantic information. The choice of dictionary plays a key role in bridging this gap: unconventional dictionaries consisting of, or learned from, the training samples themselves provide the key to obtaining state-of-the-art results and to attaching semantic meaning to sparse signal representations. Understanding the good performance of such unconventional dictionaries in turn demands new algorithmic and analytical techniques. This review paper highlights a few representative examples of how the interaction between sparse signal representation and computer vision can enrich both fields, and raises a number of open questions for further study.

1,871 citations

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23 Jun 2008TL;DR: It is shown 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.

Abstract: 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.

1,546 citations

##### Cited by

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Microsoft

^{1}TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

10,141 citations

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TL;DR: This work considers the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise, and proposes a general classification algorithm for (image-based) object recognition based on a sparse representation computed by C1-minimization.

Abstract: We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C1-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.

9,658 citations

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21 Jul 2017

TL;DR: SRGAN as mentioned in this paper proposes a perceptual loss function which consists of an adversarial loss and a content loss, which pushes the 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.

Abstract: 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.

6,884 citations

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TL;DR: In this paper, the authors prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the e1 norm.

Abstract: This article is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individuallyq We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the e1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces.

6,783 citations

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08 Oct 2016TL;DR: In this paper, the authors combine the benefits of both approaches, and propose the use of perceptual loss functions for training feed-forward networks for image style transfer, where a feedforward network is trained to solve the optimization problem proposed by Gatys et al. in real-time.

Abstract: 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 per-pixel loss between the output and ground-truth images. Parallel work has shown that high-quality images can be generated by defining and optimizing perceptual 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 Gatys et al. 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.

6,639 citations