近年来,基于张量补全的频谱制图得到了广泛研究.目前用于频谱制图的张量补全算法大多隐含地假设张量具有平衡特性,而对于非平衡张量,难以利用其低秩性估计完整的张量信息,导致补全算法性能受损.本文提出基于重叠Ket增强(Overlapping Ket Augmentation,OKA)和张量列车(Tensor Train,TT)的非平衡频谱制图算法,以解决非平衡张量在应用传统张量补全算法时性能下降的问题.首先使用OKA将低阶高维张量表示为高阶低维张量,在无信息损耗的情况下解决非平衡张量无法利用其低秩性进行张量补全的问题;然后使用TT矩阵化得到较平衡的矩阵,在维度较平衡条件下提高补全算法的精确度;最后利用高阶低维张量的低秩性,使用并行矩阵分解或基于F范数的无奇异值分解(Singular Value Decomposition Free,SVDFree)算法完成张量补全.仿真结果表明,针对非平衡张量,所提方案与现有的张量补全算法相比,可以获得更精确的无线电地图,同时所提SVDFree算法具有更低的计算复杂度.
Unbalanced Spectrum Cartography Algorithm Based on Overlapping Ket Augmentation and Tensor Train
Spectrum cartography based on tensor completion algorithms has been widely studied in recent years. Most of the current tensor completion algorithms for spectrum cartography implicitly assume that the tensor is balanced. It may not be possible to take advantage of unbalanced tensors' low-rank nature to estimate the entire tensor information,lead-ing to performance degradation. This paper proposes an unbalanced spectrum cartography algorithm based on overlapping Ket augmentation (OKA) and tensor train (TT) to address the performance degradation of unbalanced tensors when apply-ing traditional tensor completion algorithms. Firstly,OKA is used to represent the low-order high-dimensional tensor as a high-order low-dimensional tensor,which solves the problem that the unbalanced tensor is unable to utilize its low-rank na-ture for tensor completion without information loss. Secondly,the use of TT matricization to obtain more balanced matrices improves the accuracy of the completion algorithm under more balanced dimensionality conditions. Finally,using the low-rank nature of the high-order low-dimensional tensor,the tensor completion is accomplished using the parallel matrix factor-ization or Frobenius norm based singular value decomposition free (SVDFree) algorithm. Simulation results show that for unbalanced tensors,the proposed scheme can obtain more accurate radio maps compared to existing tensor completion algo-rithms,while the proposed SVDFree algorithm has lower computing complexity.
spectrum cartographytensor completiontensor trainoverlapping Ket augmentationparallel matrix factorizationsingular value decomposition
万方数据
维普
