Enhanced Solutions for the Block-Term Decomposition in Rank-$(L_{r},L_{r},1)$ Terms

The block-term decompositions (BTD) represent tensors as a linear combination of low multilinear rank terms and can be explicitly related to the Canonical Polyadic decomposition (CPD). In this paper, we introduce SECSI-BTD framework, which exploits connection between two estimate block-terms rank- $(L_{r},L_{r},1)$ BTD. proposed algorithm includes initial calculation factor estimates using SE mi-algebraic framework for approximate polyadic via SI multaneous Matrix Diagonalizations (SECSI), followed by clustering refinement procedures that return appropriate BTD terms. Moreover, new approach structure tensor based on HOSVD notation="LaTeX">$k$ -means clustering. Since does not require known but still take advantage ranks when available, it is more flexible than existing techniques in literature. Additionally, our multiple initializations, simulation results show provides accurate better convergence behavior an extensive range SNRs.