scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Lanczos Filtering in One and Two Dimensions

01 Aug 1979-Journal of Applied Meteorology (American Meteorological Society)-Vol. 18, Iss: 8, pp 1016-1022
TL;DR: In this paper, Lanczos filtering is used to reduce the amplitude of the Gibbs oscillation, which is the principal feature of the Lanczos filter, and a pair of graphs is developed that can be used to determine filter response quality given the number of weights and the value of cutoff frequency.
Abstract: A Fourier method of filtering digital data called Lanczos filtering is described Its principal feature is the use of “sigma factors” which significantly reduce the amplitude of the Gibbs oscillation A pair of graphs is developed that can be used to determine filter response quality given the number of weights and the value of the cutoff frequency, the only two inputs required by the method Examples of response functions in one and two dimensions are given and comparisons are made with response functions from other filters The simplicity of calculating the weights and the adequate response make Lanczos filtering an attractive filtering method
Citations
More filters
Proceedings ArticleDOI
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

Posted Content
TL;DR: SRGAN, a generative adversarial network (GAN) for image super-resolution (SR), is presented, to its knowledge, the first framework capable of inferring photo-realistic natural images for 4x upscaling factors and a perceptual loss function which consists of an adversarial loss and a content loss.
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.

4,404 citations


Cites background from "Lanczos Filtering in One and Two Di..."

  • ...While these filtering approaches, e.g. linear, bicubic or Lanczos [13] filtering, can be very fast, they oversimplify the SISR problem and usually yield solutions with overly smooth textures....

    [...]

  • ...linear, bicubic or Lanczos [10] filtering, can be very fast, they oversimplify the SISR problem and usually yield overly smooth solutions failing to recover the high-frequency image information....

    [...]

Proceedings ArticleDOI
27 Jun 2016
TL;DR: In this article, a very deep convolutional network inspired by VGG-net was used for image superresolution, which achieved state-of-the-art performance in accuracy.
Abstract: We present a highly accurate single-image superresolution (SR) method. Our method uses a very deep convolutional network inspired by VGG-net used for ImageNet classification [19]. We find increasing our network depth shows a significant improvement in accuracy. Our final model uses 20 weight layers. By cascading small filters many times in a deep network structure, contextual information over large image regions is exploited in an efficient way. With very deep networks, however, convergence speed becomes a critical issue during training. We propose a simple yet effective training procedure. We learn residuals only and use extremely high learning rates (104 times higher than SRCNN [6]) enabled by adjustable gradient clipping. Our proposed method performs better than existing methods in accuracy and visual improvements in our results are easily noticeable.

4,136 citations

Posted Content
TL;DR: This work presents a highly accurate single-image superresolution (SR) method using a very deep convolutional network inspired by VGG-net used for ImageNet classification and uses extremely high learning rates enabled by adjustable gradient clipping.
Abstract: We present a highly accurate single-image super-resolution (SR) method. Our method uses a very deep convolutional network inspired by VGG-net used for ImageNet classification \cite{simonyan2015very}. We find increasing our network depth shows a significant improvement in accuracy. Our final model uses 20 weight layers. By cascading small filters many times in a deep network structure, contextual information over large image regions is exploited in an efficient way. With very deep networks, however, convergence speed becomes a critical issue during training. We propose a simple yet effective training procedure. We learn residuals only and use extremely high learning rates ($10^4$ times higher than SRCNN \cite{dong2015image}) enabled by adjustable gradient clipping. Our proposed method performs better than existing methods in accuracy and visual improvements in our results are easily noticeable.

3,628 citations


Cites methods from "Lanczos Filtering in One and Two Di..."

  • ...Early methods include interpolation such as bicubic interpolation and Lanczos resampling [7] more powerful methods utilizing statistical image priors [20, 13] or internal patch recurrence [9]....

    [...]

Book
01 Nov 2002
TL;DR: A comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability.
Abstract: This comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability. It incorporates all aspects of environmental computer modeling including an historical overview of the subject, equations of motion and their approximations, a modern and clear description of numerical methods, and the determination of initial conditions using weather observations (an important science known as data assimilation). Finally, this book provides a clear discussion of the problems of predictability and chaos in dynamical systems and how they can be applied to atmospheric and oceanic systems. Professors and students in meteorology, atmospheric science, oceanography, hydrology and environmental science will find much to interest them in this book, which can also form the basis of one or more graduate-level courses.

2,240 citations

Related Papers (5)