# Joint Higher-Order Low-Rank Tensor Decompositions for Multichannel Acoustic System Compression

“Joint Higher-Order Low-Rank Tensor Decompositions for Multichannel Acoustic System Compression” (2026), by Matthias Blochberger et al. Mathematics research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Matthias Blochberger, Filip Elvander, Jan Østergaard, Toon van Waterschoot
- Published: November 5, 2026
- Field: Mathematics
- DOI: https://doi.org/10.48550/arxiv.2611.07975
- Free PDF: https://arxiv.org/pdf/2611.07975

## Abstract

Multichannel room impulse responses (RIRs) in acoustics are often long and therefore the sample count becomes large if seen as finite impulse response (FIR) filters, making storage and real-time convolution costly. Pole-zero (PZ) models are an established way to represent RIRs compactly as infinite impulse response (IIR) transfer functions. We show that a PZ model implies a low-rank canonical polyadic decomposition (CPD) of tensorized RIRs: the early reflections form a sparse rank-1 sum, while the late reverberation admits a CPD with factors determined by the poles. This motivates higher-order-tensor-based compression of RIRs via the block term decomposition (BTD), a generalization of the CPD. We propose two multichannel compression schemes: (i) a stacked multichannel block term decomposition (SMCBTD) applied to a (D+1)-mode tensor of RIRs, and (ii) a joint multichannel block term decomposition (JMCBTD) that shares subsets of factors across channels discovered by spectral clustering on factor-subspace affinity graphs. Both are optimized by an alternating higher-order orthogonal iteration (HOOI) procedure. On simulated rooms as well as measured datasets, the proposed methods achieve consistently lower reconstruction error at equal compression ratios compared to separate single-channel decompositions and a generalized low-rank approximation of matrices (GLRAM) baseline. The largest gains occur with scalar cores (i.e., CPD), supporting the PZ-to-CPD modelling link. We also find D = 3 to be a practical sweet spot, offering most of the achievable gain at moderate compute/memory cost. The compressed models enable efficient downstream multichannel convolution.

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