This paper addresses the challenge of reconstructing a 3D power spectrum map from sparse, scattered, and incomplete spectrum measurements. It proposes an integrated approach combining interpolation and block-term tensor decomposition (BTD). This approach leverages an interpolation model with the BTD structure to exploit the spatial correlation of power spectrum maps. Additionally, nuclear norm regularization is incorporated to effectively capture the low-rank characteristics. To implement this approach, a novel algorithm that combines alternating regression with singular value thresholding is developed. Analytical justification for the enhancement provided by the BTD structure in interpolating power spectrum maps is provided, yielding several important theoretical insights. The analysis explores the impact of the spectrum on the error in the proposed method and compares it to conventional local polynomial interpolation. Extensive numerical results demonstrate that the proposed method outperforms state-of-the-art methods in terms of signal source separation and power spectrum map construction, and remains stable under off-grid measurements and inhomogeneous measurement topologies.

中文翻译：

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用于频谱图构建的集成插值和块项张量分解


本文解决了从稀疏、分散和不完整的频谱测量中重建 3D 功率谱图的挑战。它提出了一种结合插值和块项张量分解（BTD）的集成方法。该方法利用具有 BTD 结构的插值模型来利用功率谱图的空间相关性。此外，还结合了核范数正则化来有效捕获低秩特征。为了实现这种方法，开发了一种将交替回归与奇异值阈值相结合的新颖算法。提供了 BTD 结构在内插功率谱图中提供的增强的分析依据，产生了几个重要的理论见解。分析探讨了频谱对所提出方法的误差的影响，并将其与传统的局部多项式插值法进行了比较。大量的数值结果表明，所提出的方法在信号源分离和功率谱图构建方面优于最先进的方法，并且在离网测量和非均匀测量拓扑下保持稳定。