A Low-Rank Tensor Completion Algorithm for Electromagnetic Spectrum Based on SIDWT

The comprehensive acquisition of electromagnetic spectrum data is crucial for applications such as cognitive radio and electromagnetic mapping in electromagnetic environment monitoring. However, the inherent limitations of spectrum sensor sampling rates and environmental unreliability often result in data loss. Existing spectrum data recovery methods predominantly adopt generic algorithms from other domains, failing to ade-quately exploit the intrinsic characteristics of spectrum signals. This paper introduces a novel low-rank autoregressive tensor com-pletion algorithm leveraging the Shift-Invariant Discrete Wavelet Transform (SIDWT) to recover and reconstruct incomplete elec-tromagnetic spectrum data. The approach focuses on minimizing the truncated nuclear norm of the SIDWT coefficient tensor, which exhibits stronger low-rank properties. Additionally, the AR(p) model is incorporated to impose temporal constraints, en-suring the reconstructed data closely approximates the original in both global and local characteristics. Additionally, to address the issue of high computational complexity, we have developed a fast algorithm. Experimental validation using real-world data demon-strates the efficacy of the proposed algorithm. It outperforms state-of-the-art algorithms on 78.1% of electromagnetic spectrum datasets and all audio signal spectrum datasets, achieving at least a 2% improvement in Relative Squared Error (RSE) compared to the best-performing baseline. Notably, under high missing rates and on TM datasets, the improvement exceeds 30%. The proposed method provides a novel solution for the completion of incomplete electromagnetic spectrum data. The proposed fast algorithm achieves approximately 40% improvement in computational speed without significant performance degradation.