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arxiv: 1906.12021 · v2 · pith:GDW6IKKCnew · submitted 2019-06-28 · 📡 eess.IV · cs.CV

Densely Residual Laplacian Super-Resolution

Saeed Anwar , Nick Barnes This is my paper

Pith reviewed 2026-05-25 13:56 UTC · model grok-4.3

classification 📡 eess.IV cs.CV
keywords image super-resolutionresidual networkdense connectionslaplacian attentionconvolutional neural networkimage restorationdeep learning
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The pith

DRLN delivers competitive super-resolution on benchmarks with a compact residual and attention architecture.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the Densely Residual Laplacian Network (DRLN) as a convolutional approach to single-image super-resolution. It combines cascading residual-on-residual blocks to direct low-frequency information toward higher-level features, dense concatenation of those blocks for deep supervision, and a Laplacian attention module to capture inter- and intra-level feature dependencies across scales. The design aims to avoid the very deep networks and long training times common in prior work while still producing strong results on low-resolution, noisy, and historical-image test sets. A sympathetic reader would care because current methods often trade off quality against computational cost, and a lighter alternative could expand practical use in image enhancement tasks.

Core claim

The Densely Residual Laplacian Network (DRLN) employs cascading residual on the residual structure to allow the flow of low-frequency information to focus on learning high and mid-level features. In addition, deep supervision is achieved via the densely concatenated residual blocks settings, which also helps in learning from high-level complex features. Moreover, Laplacian attention is proposed to model the crucial features to learn the inter and intra-level dependencies between the feature maps. Comprehensive quantitative and qualitative evaluations on low-resolution, noisy low-resolution, and real historical image benchmark datasets illustrate that the DRLN algorithm performs favorably.

What carries the argument

Cascading residual-on-residual structure with dense block concatenation and Laplacian attention, which together model multi-scale feature dependencies in a compact network.

If this is right

  • Super-resolution becomes feasible with shallower networks and shorter training schedules.
  • Multi-scale features receive explicit weighting rather than equal treatment.
  • The same structure handles clean, noisy, and historical degraded inputs without separate pipelines.
  • Low-frequency information is explicitly routed away from the main learning path.
  • High-level complex features receive direct supervision through dense skip connections.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same residual-plus-attention pattern may transfer to related restoration problems such as denoising or deblurring.
  • Laplacian attention could be tested as a drop-in module in other residual or dense vision backbones.
  • If training-time savings hold across hardware, the design may support on-device upsampling applications.
  • Scaling the number of dense blocks or attention heads offers a direct axis for future accuracy-efficiency trade-offs.

Load-bearing premise

The specific mix of residual cascades, dense connections, and Laplacian attention is what allows effective multi-scale feature modeling without needing very deep layers or extended training.

What would settle it

Running the published DRLN model on the same benchmark datasets and obtaining PSNR or SSIM scores materially below those of leading prior methods such as RCAN.

Figures

Figures reproduced from arXiv: 1906.12021 by Nick Barnes, Saeed Anwar.

Figure 1
Figure 1. Figure 1: Visual Comparisons. Sample results on URBAN100 with Bicubic (BI) degradation for 4× on “img 074” and for 8× on “img 040”. Our method recovers the structures correctly with less distortion and more faithful to the ground-truth image. purpose: 1) To learn the features at multiple sub-band frequencies and 2) to adaptively rescale features and model feature dependencies. Laplacian attention further improves th… view at source ↗
Figure 2
Figure 2. Figure 2: The detailed network architecture of the proposed Network. The top figure shows the overall architecture of our proposed network with cascading residual on the residual architecture i.e. a long skip connection, short skip connections, and cascading structures. The bottom figure presents the backbone of our network i.e. Dense Residual Laplacian Module (DRLM). residual blocks similar to [32] with a skip-conn… view at source ↗
Figure 3
Figure 3. Figure 3: Laplacian attention. Our model consists of pyramid-level attention to model the features non-linearly. The Laplacian attention weights the residual features at different sub-frequency-bands. total variation [40] and adversarial [16], [35]. To be fair with the competing state-of-the-art methods [5], [7], [15], we also choose `1 loss function for our network optimization. Now, for a batch of N training pairs… view at source ↗
Figure 4
Figure 4. Figure 4: Parameters vs. performance. Comparisons are presented on the MANGA109 [43] for 4× super-resolution. To produce attention differently at the Laplacian pyramids in the DRLM, we use a global descriptor to capture the statistics expressing the entire image. The proposed Laplacian pyramid weights the sub-band features of high importance progressively in each DRLM. The global descriptor takes the output from the… view at source ↗
Figure 6
Figure 6. Figure 6: Visual comparison for 4×. Super-resolution comparison on sample images with sharp edges and texture, taken from URBAN100 [45] and MANGA109 [43] for the scale of 4×. The sharpness of the edges on the objects and textures restored by our method is the best. 4.2 Ablation Studies 4.2.1 Influence of the skip connections Skip connections are the backbone of the current state of the art network [7], [8], [9], [15… view at source ↗
Figure 7
Figure 7. Figure 7: Visual comparison for 8×. Comparisons on images with fine details for a high upsampling factor of 8× on URBAN100 [45] and MANGA109 [43]. The best results are in bold. EDSR [5] and the runtime is less as compared to RCAN [7] i.e. the time taken by RCAN for an image of size 824×1168 on average is 1.14s opposed to our method 0.045s on MANGA109 [45] for 4×. This efficiency is due to the fact that our method ma… view at source ↗
Figure 8
Figure 8. Figure 8: Blur-Downscale (BD) degradation. Comparison on sample images with sharp edges and texture, taken from URBAN100 and SET14 datasets for the scale of 3×. The sharpness of the edges on the objects and textures restored by our method is the best. TABLE 3 Quantitative results with blur-down degradation. The best results are highlighted with red color while the blue color represents the second best. SET5 [46] SET… view at source ↗
Figure 9
Figure 9. Figure 9: Noisy SR visual Comparison on BSD100. Textures on the birds are much better reconstructed, and the noise removed by our method as compared to the IRCNN [21] and RCAN [7] for σ = 10. Noisy GT BM3D-SR [54] BM3D-SRNI [55] Ours σ = 20 PSNR/SSIM 25.05/0.5868 25.31/0.6206 27.03/0.7330 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Noisy visual comparison on Llama. Textures on the fur, and on rocks in the background are much better reconstructed in our result as compared to the conventional BM3D-SR and BM3D-SRNI [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Noisy super-resolution. The plots show average PSNR as functions of noise sigma. Our method consistently improves over spe￾cific noisy super-resolution methods and CNN for all σ levels. performance gain over all methods in general, and RDN [15] and RCAN [7] particular. The average PSNR gain over both the mentioned methods for 3× super-resolution of blur-down degraded images is 0.55dB and 0.33dB for all th… view at source ↗
Figure 13
Figure 13. Figure 13: Limitation. A failure case for super-resolution of 8×. Our algorithm is not able to create finer details if the input low-resolution images lack sufficient high-frequency details. 4.5 Limitations Our model has shown the ability to render sharp and clean images for all upsampling scales; however, it struggles to “hallucinate” finer details. For example, an image with 8× is shown in Fig￾ure 13, the top of t… view at source ↗
read the original abstract

Super-Resolution convolutional neural networks have recently demonstrated high-quality restoration for single images. However, existing algorithms often require very deep architectures and long training times. Furthermore, current convolutional neural networks for super-resolution are unable to exploit features at multiple scales and weigh them equally, limiting their learning capability. In this exposition, we present a compact and accurate super-resolution algorithm namely, Densely Residual Laplacian Network (DRLN). The proposed network employs cascading residual on the residual structure to allow the flow of low-frequency information to focus on learning high and mid-level features. In addition, deep supervision is achieved via the densely concatenated residual blocks settings, which also helps in learning from high-level complex features. Moreover, we propose Laplacian attention to model the crucial features to learn the inter and intra-level dependencies between the feature maps. Furthermore, comprehensive quantitative and qualitative evaluations on low-resolution, noisy low-resolution, and real historical image benchmark datasets illustrate that our DRLN algorithm performs favorably against the state-of-the-art methods visually and accurately.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes the Densely Residual Laplacian Network (DRLN) for single-image super-resolution. It introduces a cascading residual-on-residual structure to allow low-frequency information to flow while focusing on high- and mid-level features, densely concatenated residual blocks to achieve deep supervision and learn from complex high-level features, and a Laplacian attention module to model inter- and intra-level feature dependencies. The authors assert that this combination yields a compact network that avoids the very deep architectures and long training times of prior methods while performing favorably against state-of-the-art approaches on low-resolution, noisy low-resolution, and real historical image benchmarks, both quantitatively and qualitatively.

Significance. If the efficiency and accuracy claims are substantiated by the experiments, the work could advance practical super-resolution by demonstrating that residual-on-residual cascading plus dense connections and Laplacian attention can deliver competitive multi-scale modeling at lower architectural cost than EDSR/RDN/RCAN-style networks. The introduction of the Laplacian attention module is a distinct architectural element that could be reusable. However, the abstract supplies no parameter counts, FLOPs, training times, ablation results, or numerical metrics, so the significance cannot be assessed from the provided text.

major comments (2)
  1. [Abstract] Abstract: the central efficiency claim ('often require very deep architectures and long training times' and 'compact') is asserted without any supporting numbers on depth, parameter count, FLOPs, or training time relative to EDSR, RDN, or RCAN; this is load-bearing for the stated advantage of the cascading residual-on-residual + dense concatenation + Laplacian attention combination.
  2. [Abstract] Abstract: the claim that DRLN 'performs favorably against the state-of-the-art methods visually and accurately' is made without any quantitative results, tables, error bars, or dataset-specific metrics; the empirical evaluation that underpins the 'performs favorably' conclusion is therefore not verifiable from the given text.
minor comments (1)
  1. [Abstract] Abstract: 'Laplacian attention' is introduced as a novel module without a definition, equation, or reference to Laplacian pyramid or attention literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their valuable feedback. We address the two major comments regarding the abstract below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central efficiency claim ('often require very deep architectures and long training times' and 'compact') is asserted without any supporting numbers on depth, parameter count, FLOPs, or training time relative to EDSR, RDN, or RCAN; this is load-bearing for the stated advantage of the cascading residual-on-residual + dense concatenation + Laplacian attention combination.

    Authors: We agree that the abstract would benefit from including specific quantitative evidence for the efficiency claims. In the revised version, we will update the abstract to include key figures such as parameter counts and comparisons to prior methods. revision: yes

  2. Referee: [Abstract] Abstract: the claim that DRLN 'performs favorably against the state-of-the-art methods visually and accurately' is made without any quantitative results, tables, error bars, or dataset-specific metrics; the empirical evaluation that underpins the 'performs favorably' conclusion is therefore not verifiable from the given text.

    Authors: We acknowledge this point. The manuscript provides extensive quantitative evaluations along with qualitative results. To make the abstract self-contained, we will revise it to include representative quantitative metrics supporting the favorable performance. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical SR architecture with no derivation chain or fitted predictions.

full rationale

The paper introduces DRLN, a CNN for super-resolution, and supports its claims solely through quantitative/qualitative experiments on benchmark datasets. No equations, first-principles derivations, or 'predictions' appear in the provided text. The architecture (cascading residual-on-residual, dense concatenation, Laplacian attention) is presented as a design choice evaluated empirically, not derived from or equivalent to its own inputs. Any self-citations to prior SR methods are external benchmarks, not load-bearing justifications that reduce the central claim to a self-referential fit. The efficiency assertions ('compact', 'no very deep architectures') are unquantified in the abstract but remain an evidence gap rather than circularity. This matches the default case of an empirical paper that is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Central claim rests on standard deep-learning assumptions plus the effectiveness of three newly combined architectural choices whose benefit is asserted via benchmark comparison.

free parameters (1)
  • network depth and channel counts
    Number of residual blocks, feature channels, and attention scales chosen to achieve reported performance.
axioms (1)
  • domain assumption Convolutional layers can extract hierarchical image features when trained with gradient descent.
    Invoked implicitly by any CNN super-resolution method.
invented entities (1)
  • Laplacian attention module no independent evidence
    purpose: To model crucial features and capture inter- and intra-level dependencies between feature maps.
    New component introduced by the paper; no independent evidence supplied in abstract.

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Forward citations

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Reference graph

Works this paper leans on

57 extracted references · 57 canonical work pages · cited by 1 Pith paper

  1. [1]

    Low resolution face recognition across variations in pose and illumination,

    S. P. Mudunuri and S. Biswas, “Low resolution face recognition across variations in pose and illumination,” TPAMI, 2016

    work page 2016

  2. [2]

    Super-resolution in medical imaging,

    H. Greenspan, “Super-resolution in medical imaging,” CJ, 2008

    work page 2008

  3. [3]

    Digital image forensics via intrinsic fingerprints,

    A. Swaminathan, M. Wu, and K. R. Liu, “Digital image forensics via intrinsic fingerprints,”TIFS, 2008

    work page 2008

  4. [5]

    Enhanced deep residual networks for single image super-resolution,

    B. Lim, S. Son, H. Kim, S. Nah, and K. M. Lee, “Enhanced deep residual networks for single image super-resolution,” in CVPRW, 2017

    work page 2017

  5. [6]

    Fast and accurate image super-resolution with deep laplacian pyramid networks,

    W.-S. Lai, J.-B. Huang, N. Ahuja, and M.-H. Yang, “Fast and accurate image super-resolution with deep laplacian pyramid networks,” TPAMI, 2018

    work page 2018

  6. [7]

    Image super- resolution using very deep residual channel attention networks,

    Y . Zhang, K. Li, K. Li, L. Wang, B. Zhong, and Y . Fu, “Image super- resolution using very deep residual channel attention networks,” ECCV, 2018

    work page 2018

  7. [8]

    Fast, accurate, and, lightweight super-resolution with cascading residual network,

    N. Ahn, B. Kang, and K.-A. Sohn, “Fast, accurate, and, lightweight super-resolution with cascading residual network,” ECCV, 2018

    work page 2018

  8. [9]

    Accurate image super-resolution using very deep convolutional networks,

    J. Kim, J. Kwon Lee, and K. Mu Lee, “Accurate image super-resolution using very deep convolutional networks,” in CVPR, 2016

    work page 2016

  9. [10]

    Deep laplacian pyramid networks for fast and accurate superresolution,

    W.-S. Lai, J.-B. Huang, N. Ahuja, and M.-H. Yang, “Deep laplacian pyramid networks for fast and accurate superresolution,” in CVPR, 2017

    work page 2017

  10. [11]

    Image super-resolution using deep convolutional networks,

    C. Dong, C. C. Loy, K. He, and X. Tang, “Image super-resolution using deep convolutional networks,” TPAMI, 2016

    work page 2016

  11. [12]

    Image super-resolution via deep recursive residual network,

    Y . Tai, J. Yang, and X. Liu, “Image super-resolution via deep recursive residual network,” in CVPR, 2017

    work page 2017

  12. [13]

    Deeply-recursive convolutional network for image super-resolution,

    J. Kim, J. Kwon Lee, and K. Mu Lee, “Deeply-recursive convolutional network for image super-resolution,” in CVPR, 2016

    work page 2016

  13. [14]

    Image super-resolution using dense skip connections,

    T. Tong, G. Li, X. Liu, and Q. Gao, “Image super-resolution using dense skip connections,” in ICCV, 2017

    work page 2017

  14. [15]

    Residual dense network for image super-resolution,

    Y . Zhang, Y . Tian, Y . Kong, B. Zhong, and Y . Fu, “Residual dense network for image super-resolution,” in CVPR, 2018

    work page 2018

  15. [16]

    Photo-realistic single image super-resolution using a generative adversarial network

    C. Ledig, L. Theis, F. Husz ´ar, J. Caballero, A. Cunningham, A. Acosta, A. P. Aitken, A. Tejani, J. Totz, Z. Wang et al. , “Photo-realistic single image super-resolution using a generative adversarial network.”

    work page

  16. [17]

    Ram: Residual attention module for single image super-resolution,

    J.-H. Kim, J.-H. Choi, M. Cheon, and J.-S. Lee, “Ram: Residual attention module for single image super-resolution,” arXiv, 2018

    work page 2018

  17. [18]

    Deep backprojection net- works for super-resolution,

    M. Haris, G. Shakhnarovich, and N. Ukita, “Deep backprojection net- works for super-resolution,” in CVPR, 2018

    work page 2018

  18. [19]

    Delving deep into rectifiers: Surpassing human-level performance on imagenet classification,

    K. He, X. Zhang, S. Ren, and J. Sun, “Delving deep into rectifiers: Surpassing human-level performance on imagenet classification,” in ICCV, 2015

    work page 2015

  19. [20]

    Accelerating the super-resolution convolutional neural network,

    C. Dong, C. C. Loy, and X. Tang, “Accelerating the super-resolution convolutional neural network,” in ECCV, 2016

    work page 2016

  20. [21]

    Learning deep cnn denoiser prior for image restoration,

    K. Zhang, W. Zuo, S. Gu, and L. Zhang, “Learning deep cnn denoiser prior for image restoration,” in CVPR, 2017

    work page 2017

  21. [22]

    Learning a single convolutional super- resolution network for multiple degradations,

    K. Zhang, W. Zuo, and L. Zhang, “Learning a single convolutional super- resolution network for multiple degradations,” in CVPR, 2018

    work page 2018

  22. [23]

    Memnet: A persistent memory network for image restoration,

    Y . Tai, J. Yang, X. Liu, and C. Xu, “Memnet: A persistent memory network for image restoration,” in CVPR, 2017

    work page 2017

  23. [24]

    Densely connected convolutional networks,

    G. Huang, Z. Liu, L. van der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” in CVPR, 2017

    work page 2017

  24. [25]

    Image super resolution based on fusing multiple convolution neural networks,

    H. Ren, M. El-Khamy, and J. Lee, “Image super resolution based on fusing multiple convolution neural networks,” in CVPRW, 2017

    work page 2017

  25. [26]

    Single image super- resolution via cascaded multi-scale cross network,

    Y . Hu, X. Gao, J. Li, Y . Huang, and H. Wang, “Single image super- resolution via cascaded multi-scale cross network,” arXiv, 2018

    work page 2018

  26. [27]

    Fast and accurate single image super- resolution via information distillation network,

    Z. Hui, X. Wang, and X. Gao, “Fast and accurate single image super- resolution via information distillation network,” in CVPR, 2018

    work page 2018

  27. [28]

    Learning a deep convolutional network for image super-resolution,

    C. Dong, C. Loy, K. He, and X. Tang, “Learning a deep convolutional network for image super-resolution,” in ECCV, 2014

    work page 2014

  28. [29]

    Rectifier nonlinearities improve neural network acoustic models,

    A. L. Maas, A. Y . Hannun, and A. Y . Ng, “Rectifier nonlinearities improve neural network acoustic models,” in ICML, 2013

    work page 2013

  29. [30]

    Unsupervised representation learning with deep convolutional generative adversarial networks,

    A. Radford, L. Metz, and S. Chintala, “Unsupervised representation learning with deep convolutional generative adversarial networks,”arXiv, 2015

    work page 2015

  30. [31]

    Generative adversarial nets,

    I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y . Bengio, “Generative adversarial nets,” in NIPS, 2014

    work page 2014

  31. [32]

    Deep residual learning for image recognition,

    K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in CVPR, 2016

    work page 2016

  32. [33]

    Enhancenet: Single image super-resolution through automated texture synthesis,

    M. S. Sajjadi, B. Sch ¨olkopf, and M. Hirsch, “Enhancenet: Single image super-resolution through automated texture synthesis,” in ICCV, 2017

    work page 2017

  33. [34]

    Srfeat: Single image super-resolution with feature discrimination,

    S.-J. Park, H. Son, S. Cho, K.-S. Hong, and S. Lee, “Srfeat: Single image super-resolution with feature discrimination,” in ECCV, 2018

    work page 2018

  34. [35]

    Esrgan: Enhanced super-resolution generative adversarial networks,

    X. Wang, K. Yu, S. Wu, J. Gu, Y . Liu, C. Dong, C. C. Loy, Y . Qiao, and X. Tang, “Esrgan: Enhanced super-resolution generative adversarial networks,” ECCV, 2018

    work page 2018

  35. [36]

    The relativistic discriminator: a key element missing from standard gan,

    A. Jolicoeur-Martineau, “The relativistic discriminator: a key element missing from standard gan,” arXiv, 2018

    work page 2018

  36. [37]

    Recurrent models of visual attention,

    V . Mnih, N. Heess, A. Graves et al. , “Recurrent models of visual attention,” in NIPS, 2014

    work page 2014

  37. [38]

    A learned representation for artistic style,

    V . Dumoulin, J. Shlens, and M. Kudlur, “A learned representation for artistic style,” ICLR, 2017

    work page 2017

  38. [39]

    Real-time single image and video super- resolution using an efficient sub-pixel convolutional neural network,

    W. Shi, J. Caballero, F. Husz ´ar, J. Totz, A. P. Aitken, R. Bishop, D. Rueckert, and Z. Wang, “Real-time single image and video super- resolution using an efficient sub-pixel convolutional neural network,” in CVPR, 2016

    work page 2016

  39. [40]

    Formresnet: formatted residual learning for image restoration,

    J. Jiao, W.-C. Tu, S. He, and R. W. Lau, “Formresnet: formatted residual learning for image restoration,” in CVPRW, 2017

    work page 2017

  40. [41]

    Residual attention network for image classification,

    F. Wang, M. Jiang, C. Qian, S. Yang, C. Li, H. Zhang, X. Wang, and X. Tang, “Residual attention network for image classification,” in CVPR, 2017

    work page 2017

  41. [42]

    Show and tell: A neural image caption generator,

    O. Vinyals, A. Toshev, S. Bengio, and D. Erhan, “Show and tell: A neural image caption generator,” in CVPR, 2015

    work page 2015

  42. [43]

    Manga109 dataset and creation of metadata,

    A. Fujimoto, T. Ogawa, K. Yamamoto, Y . Matsui, T. Yamasaki, and K. Aizawa, “Manga109 dataset and creation of metadata,” in MANPU, 2016

    work page 2016

  43. [44]

    Squeeze-and-excitation networks,

    J. Hu, L. Shen, and G. Sun, “Squeeze-and-excitation networks,” in CVPR, 2018

    work page 2018

  44. [46]

    Low- complexity single-image super-resolution based on nonnegative neighbor embedding,

    M. Bevilacqua, A. Roumy, C. Guillemot, and M. L. Alberi-Morel, “Low- complexity single-image super-resolution based on nonnegative neighbor embedding,” 2012

    work page 2012

  45. [47]

    On single image scale-up using sparse-representations,

    R. Zeyde, M. Elad, and M. Protter, “On single image scale-up using sparse-representations,” in ICCS, 2010

    work page 2010

  46. [48]

    A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,

    D. Martin, C. Fowlkes, D. Tal, and J. Malik, “A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics,” in ICCV, 2001

    work page 2001

  47. [49]

    Ntire 2017 challenge on single image super-resolution: Methods and results,

    R. Timofte, E. Agustsson, L. Van Gool, M.-H. Yang, L. Zhang, B. Lim, S. Son, H. Kim, S. Nah, K. M. Lee et al., “Ntire 2017 challenge on single image super-resolution: Methods and results,” in CVPRW, 2017

    work page 2017

  48. [50]

    Adam: A method for stochastic optimization,

    D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv, 2014

    work page 2014

  49. [51]

    Automatic differentiation in pytorch,

    A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer, “Automatic differentiation in pytorch,” 2017

    work page 2017

  50. [52]

    Deep networks for image super-resolution with sparse prior,

    Z. Wang, D. Liu, J. Yang, W. Han, and T. Huang, “Deep networks for image super-resolution with sparse prior,” in ICCV, 2015

    work page 2015

  51. [53]

    A statistical prediction model based on sparse representations for single image super-resolution,

    T. Peleg and M. Elad, “A statistical prediction model based on sparse representations for single image super-resolution,” TIP, 2014

    work page 2014

  52. [54]

    Image denoising by sparse 3-D transform-domain collaborative filtering,

    K. Dabov, A. F., V . Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-D transform-domain collaborative filtering,” 2007

    work page 2007

  53. [55]

    Super-resolving noisy images,

    A. Singh, F. Porikli, and N. Ahuja, “Super-resolving noisy images,” in CVPR, 2014

    work page 2014

  54. [56]

    A non-local algorithm for image denoising,

    A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” in CVPR, 2005

    work page 2005

  55. [57]

    Psyco: Manifold span reduction for super resolution,

    E. P ´erez-Pellitero, J. Salvador, J. Ruiz-Hidalgo, and B. Rosenhahn, “Psyco: Manifold span reduction for super resolution,” in CVPR, 2016

    work page 2016

  56. [58]

    Imagenet: A large-scale hierarchical image database,

    J. Deng, W. Dong, R. Socher, L.-J. Li, K. Li, and L. Fei-Fei, “Imagenet: A large-scale hierarchical image database,” 2009

    work page 2009

  57. [59]

    Single image super-resolution from transformed self-exemplars,

    J.-B. Huang, A. Singh, and N. Ahuja, “Single image super-resolution from transformed self-exemplars,” in CVPR, 2015

    work page 2015