Relative impulse responses (ReIRs) have several applications in speech enhancement, noise suppression and source localization for multi-channel speech processing in reverberant environments. Estimating the ReIRs can be reduced to a system identification problem. A system identification method using an empirical Bayes framework is proposed and its application for spatial source subtraction in audio signal processing is evaluated. The proposed estimator allows for incorporating prior structure information of the system into the estimation procedure, leading to an improved performance especially in the presence of noise. The estimator utilizes the sparse Bayesian learning algorithm with appropriate priors to characterize both the early reflections and reverberant tails. The mean squared error of the proposed estimator is studied and an extensive experimental study with real-world recordings is conducted to show the efficacy of the proposed approach over other competing approaches.
