Integrated Interpolation and Block-Term Tensor Decomposition for Spectrum Map Construction

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.