Bayesian regularization and nonnegative deconvolution for time delay estimation

Nonnegative Deconvolution (BRAND) for accurately and robustly estimating acoustic room impulse responses for applications such as time-delay estimation and echo cancellation. Similar to conven-tional deconvolution methods, BRAND estimates the coefficients of convolutive finite-impulse-response (FIR) filters using least-square optimization. However, BRAND exploits the nonnegative, sparse structure of acoustic room impulse responses with nonnegativity constraints and 1-norm sparsity regularization on the filter coef-ficients. The optimization problem is modeled within the context of a probabilistic Bayesian framework, and expectation-maximiza-tion (EM) is used to derive efficient update rules for estimating the optimal regularization parameters. BRAND is demonstrated on two representative examples, subsample time-delay estimation in reverberant environments and acoustic echo cancellation. The results presented in this paper show the advantages of BRAND in high temporal resolution and robustness to ambient noise compared with other conventional techniques. Index Terms—Bayesian regularization, echo cancellation, non-negative deconvolution, time-delay estimation. I