基于低秩张量补全的多声道音频信号恢复方法

多声道音频信号在采集、压缩、传输过程中可能造成音频数据丢失，为了确保给听众带来更真实的听觉感受，该文提出一种基于低秩张量补全的音频丢失数据恢复方法。首先，把多声道音频信号表示为一个张量；其次，把张量补全作为一个凸优化问题建模，利用松弛技术和变量分离技术得到闭合的增强拉格朗日函数；最后，通过交替迭代方法求解得到恢复的音频张量。在不同数据丢失率的实验中，通过与线性预测、加权优化的CANDECOMP /PARAFAC分解方法进行对比分析，表明利用张量补全方法具有更高的音频信号恢复精度，隐藏参考和基准的多激励测试结果也显示低秩张量补全方法能够有效地恢复多声道音频的丢失数据，从而获得更好的听觉效果。

Low Rank Tensor Completion for Recovering Missing Data in Multi-channel Audio Signal

The data maybe miss due to problems in the acquisition, compression or transmission process of multi- channel audio signal. In order to take audiences real auditory sense, an approach of signal recovery based on low rank tensor completion is proposed. First, multi-channel audio signal is represented as a signal tensor. Second, tensor completion is formulated as a convex optimization problem. A closed form for augmented Lagrangian function is obtained via relaxation technique and separation of variables technique. At last, the audio tensor is recovered by alternating iteration. In experiments of varying number of missing entries, the comparisons show that the proposed method is more accurate than linear prediction and CANDECOMP/PARAFAC weighted optimization. The results of multiple stimuli with hidden reference and anchor indicate that low rank tensor completion method is validated for multi-channel audio signal recovery. The better auditory effects are obtained by recovered audio.