This paper reviews the first NTIRE challenge on quality enhancement of compressed video, with a focus on the proposed methods and results. In this challenge, the new Large-scale Diverse Video (LDV) dataset is employed. The challenge has three tracks. Tracks 1 and 2 aim at enhancing the videos compressed by HEVC at a fixed QP, while Track 3 is designed for enhancing the videos compressed by x265 at a fixed bit-rate. Besides, the quality enhancement of Tracks 1 and 3 targets at improving the fidelity (PSNR), and Track 2 targets at enhancing the perceptual quality. The three tracks totally attract 482 registrations. In the test phase, 12 teams, 8 teams and 11 teams submitted the final results of Tracks 1, 2 and 3, respectively. The proposed methods and solutions gauge the state-of-the-art of video quality enhancement. The homepage of the challenge: https://github.com/RenYang-home/NTIRE21_VEnh
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