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

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