基于块项分解模型的多维谐波信号张量补全算法
A Block Term Decomposition Model Based Algorithm for Tensor Completion of Multidimensional Harmonic Signals
AI总结：
针对多维谐波信号补全，提出基于块项分解（BTD）模型与交替方向乘子法的算法，以描述复杂谐波对应关系并实现低秩优化，在仿真和Sub-6GHz CSI补全中验证了有效性。
摘要：
我们考虑多维谐波（MH）信号不完整观测的张量数据补全。现有的基于张量的MH检索（MHR）技术大多采用典范多项式分解（CPD）来建模不同模式间谐波的简单“一对一”对应关系，与之不同，我们在此使用更灵活的块项分解（BTD）模型，该模型可用于描述不同模式间若干组谐波的复杂相互对应关系。我们为张量补全任务建立了一个优化原则，旨在以最小二乘意义拟合BTD模型，并受限于汉克尔化的MH分量的秩最小化，同时提出了一种基于交替方向乘子法的算法，其有效性和适用性通过数值仿真以及Sub-6GHz信道状态信息（CSI）补全的应用得到了验证。
英文摘要：
We consider tensor data completion of an incomplete observation of multidimensional harmonic (MH) signals. Unlike existing tensor-based techniques for MH retrieval (MHR), which mostly adopt the canonical polyadic decomposition (CPD) to model the simple "one-to-one" correspondence among harmonics across difference modes, we herein use the more flexible block term decomposition (BTD) model that can be used to describe the complex mutual correspondences among several groups of harmonics across different modes. An optimization principle that aims to fit the BTD model in the least squares sense, subject to rank minimization of hankelized MH components, is set up for the tensor completion task, and an algorithm based on alternating direction method of multipliers is proposed, of which the effectiveness and applicability are validated through both numerical simulations and an application in Sub-6GHz channel state information (CSI) completion.
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