Low-Rank Room Impulse Response Estimation

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