Low-Rank Room Impulse Response Estimation

Martin Jälmby*, Filip Elvander, Toon Van Waterschoot

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
17 Downloads (Pure)


In this paper we consider low-rank estimation of room impulse responses (RIRs). Inspired by a physics-driven room-acoustical model, we propose an estimator of RIRs that promotes a low-rank structure for a matricization, or reshaping, of the estimated RIR. This low-rank prior acts as a regularizer for the inverse problem of estimating an RIR from input-output observations, preventing overfitting and improving estimation accuracy. As directly enforcing a low rank of the estimate results is an NP-hard problem, we consider two different relaxations, one using the nuclear norm, and one using the recently introduced concept of quadratic envelopes. Both relaxations allow for implementing the proposed estimator using a first-order algorithm with convergence guarantees. When evaluated on both synthetic and recorded RIRs, it is shown that under noisy output conditions, or when the spectral excitation of the input signal is poor, the proposed estimator outperforms comparable existing methods. The performance of the two low-rank relaxations methods is similar, but the quadratic envelope has the benefit of superior robustness to the choice of regularization hyperparameter in the case when the signal-to-noise ratio is unknown. The performance of the proposed method is compared to that of ordinary least squares, Tikhonov least squares, as well as the Cramér-Rao lower bound (CRLB).

Original languageEnglish
Pages (from-to)957-969
Number of pages13
JournalIEEE/ACM Transactions on Audio Speech and Language Processing
Publication statusPublished - 2023
MoE publication typeA1 Journal article-refereed


  • Low-rank modeling
  • quadratic envelopes
  • room impulse responses


Dive into the research topics of 'Low-Rank Room Impulse Response Estimation'. Together they form a unique fingerprint.

Cite this