发表机构
Southwest University; Chongqing Normal University（西南大学; 重庆师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出反射卷积核范数最小化（RCNNM），以反射替代循环平移，实现鲁棒张量补全，在随机采样和稀疏污染下保证精确恢复，并在边界PSNR上平均提升3.26 dB。
AI 中文摘要
鲁棒张量补全旨在从被稀疏粗差破坏的部分观测中恢复多维数据。现有的卷积低秩模型通常利用循环延拓构造平移副本，这会给有限非周期数据引入人为的环绕邻域。我们提出反射卷积核范数最小化（RCNNM），用端点不重复的反射替代循环平移。由此产生的提升具有非均匀条目重数，并满足加权Gram恒等式，该恒等式同时支持恢复分析和优化方法。在随机采样和稀疏污染条件下，我们建立了底层张量和稀疏误差的高概率精确恢复，以及在有界稠密扰动下的稳定性。我们进一步开发了一种两块的ADMM算法，其中张量更新具有闭式逐条目形式，而奇异值阈值通过较小的右Gram矩阵实现。在合成张量、BSDS彩色图像和CAVE多光谱图像上的实验表明，RCNNM始终优于其循环提升对应方法，在图像边界附近的提升最为明显。特别是，平均边界PSNR改进达到3.26 dB，同时全局重建质量保持竞争力。
英文摘要
Robust tensor completion recovers multidimensional data from partial observations corrupted by sparse gross errors. Existing convolutional low-rank models typically construct translated copies using circular continuation, which introduces artificial wrap-around neighborhoods for finite nonperiodic data. We propose reflective convolution nuclear norm minimization (RCNNM), which replaces circular shifts with endpoint-nonrepeating reflection. The resulting lifting has nonuniform entry multiplicities and satisfies a weighted Gram identity that supports both the recovery analysis and the optimization method. Under random sampling and sparse corruption, we establish high-probability exact recovery of the underlying tensor and sparse errors, together with stability under bounded dense perturbations. We further develop a two-block ADMM with a closed-form entrywise tensor update, while singular-value thresholding is implemented through the smaller right Gram matrix. Experiments on synthetic tensors, BSDS color images, and CAVE multispectral images show that RCNNM consistently improves over its circular-lifting counterpart, with the clearest gains near image boundaries. In particular, average boundary-PSNR improvements reach 3.26 dB while global reconstruction quality remains competitive.
Comments24 pages, 7 figures, 6 tables
