Empirical Bayes based relative impulse response estimation.

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.

A unified framework for sparse non-negative least squares using multiplicative updates and the non-negative matrix factorization problem.

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the sparse codes. We show that the proposed framework encompasses a large class of S-NNLS algorithms and provide a computationally efficient inference procedure based on multiplicative update rules. Such update rules are convenient for solving large sets of S-NNLS problems simultaneously, which is required in contexts like sparse non-negative matrix factorization (S-NMF). We provide theoretical justification for the proposed approach by showing that the local minima of the objective function being optimized are sparse and the S-NNLS algorithms presented are guaranteed to converge to a set of stationary points of the objective function. We then extend our framework to S-NMF, showing that our framework leads to many well known S-NMF algorithms under specific choices of prior and providing a guarantee that a popular subclass of the proposed algorithms converges to a set of stationary points of the objective function. Finally, we study the performance of the proposed approaches on synthetic and real-world data.