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Beyond Deep Residual Learning for Image Restoration: Persistent Homology-Guided Manifold Simplification

19 Nov 2016arXiv:1611.06345archive 2025-07-28

Woong Bae, Jaejun Yoo, Jong Chul Ye

The latest deep learning approaches perform better than the state-of-the-art signal processing approaches in various image restoration tasks. However, if an image contains many patterns and structures, the performance of these CNNs is still inferior. To address this issue, here we propose a novel feature space deep residual learning algorithm that outperforms the existing residual learning. The main idea is originated from the observation that the performance of a learning algorithm can be improved if the input and/or label manifolds can be made topologically simpler by an analytic mapping to a feature space. Our extensive numerical studies using denoising experiments and NTIRE single-image super-resolution (SISR) competition demonstrate that the proposed feature space residual learning outperforms the existing state-of-the-art approaches. Moreover, our algorithm was ranked third in NTIRE competition with 5-10 times faster computational time compared to the top ranked teams. The source code is available on page : https://github.com/iorism/CNN.git

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Tasks

Color Image DenoisingDenoisingImage RestorationImage Super-ResolutionSuper-Resolution

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Color Image Denoising CBSD68 sigma50 DnCNN PSNR 28.01 #10 of 18 Archive leaderboard report
Image Super-Resolution BSD100 - 4x upscaling Manifold Simplification PSNR 27.66 #29 of 71 Archive leaderboard report
Image Super-Resolution BSD100 - 4x upscaling Manifold Simplification SSIM 0.7380 #29 of 71 Archive leaderboard report
Image Super-Resolution Set14 - 4x upscaling Manifold Simplification PSNR 28.80 #51 of 104 Archive leaderboard report
Image Super-Resolution Set14 - 4x upscaling Manifold Simplification SSIM 0.7856 #51 of 104 Archive leaderboard report
Image Super-Resolution Urban100 - 4x upscaling Manifold Simplification PSNR 26.42 #39 of 65 Archive leaderboard report
Image Super-Resolution Urban100 - 4x upscaling Manifold Simplification SSIM 0.7940 #39 of 65 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

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