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arXiv 2306.09652cs.CVcs.NAmath.NA
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一种用于彩色视频修复问题的新型低秩学习鲁棒四元数张量补全方法及快速算法

A New Low-Rank Learning Robust Quaternion Tensor Completion Method for Color Video Inpainting Problem and Fast Algorithms

Jiangsu Normal University(江苏师范大学)

Zhigang Jia, Jingfei Zhu

AI总结:

针对彩色视频修复中难同时保通道耦合与帧演化的问题,提出鲁棒四元数张量补全模型及低秩学习变体,搭配收敛快速算法,实验指标优于现有方法。

摘要:

彩色视频修复问题是现代成像科学中最具挑战性的问题之一,其目标是从一小部分可能含噪的像素中恢复彩色视频。然而,目前能够同时保留彩色通道耦合性与彩色视频帧演化特性的鲁棒模型较为匮乏。本文提出一种新型鲁棒四元数张量补全(RQTC)模型以解决这一难题,并推导了精确恢复理论。该模型的核心思路是构建四元数张量优化模型,恢复代表目标彩色视频的低秩四元数张量与代表噪声的稀疏四元数张量,对满足低秩先验假设的高维数据恢复效率很高。针对不具备低秩特性的情况,本文提出一种新型低秩学习RQTC模型,通过四元数学习方法将分类得到的相似块重排为满足低秩先验假设的更小张量。本文还提出了具备全局收敛性保证的快速算法。数值实验中,所提方法成功恢复彩色视频,消除了色彩污染并保持了视频场景的连续性,其解在PSNR和SSIM指标上的质量优于现有最优算法。

英文摘要:

The color video inpainting problem is one of the most challenging problem in the modern imaging science. It aims to recover a color video from a small part of pixels that may contain noise. However, there are less of robust models that can simultaneously preserve the coupling of color channels and the evolution of color video frames. In this paper, we present a new robust quaternion tensor completion (RQTC) model to solve this challenging problem and derive the exact recovery theory. The main idea is to build a quaternion tensor optimization model to recover a low-rank quaternion tensor that represents the targeted color video and a sparse quaternion tensor that represents noise. This new model is very efficient to recover high dimensional data that satisfies the prior low-rank assumption. To solve the case without low-rank property, we introduce a new low-rank learning RQTC model, which rearranges similar patches classified by a quaternion learning method into smaller tensors satisfying the prior low-rank assumption. We also propose fast algorithms with global convergence guarantees. In numerical experiments, the proposed methods successfully recover color videos with eliminating color contamination and keeping the continuity of video scenery, and their solutions are of higher quality in terms of PSNR and SSIM values than the state-of-the-art algorithms.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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