Bayesian Regularization and Nonnegative Deconvolution for Time Delay Estimation

Bayesian Regularization and Nonnegative Deconvolution (BRAND) is proposed for estimating time delays of acoustic signals in reverberant environments. Sparsity of the nonnegative filter coefficients is enforced using an L1-norm regularization. A probabilistic generative model is used to simultaneously estimate the regularization parameters and filter coefficients from the signal data. Iterative update rules are derived under a Bayesian framework using the Expectation-Maximization procedure. The resulting time delay estimation algorithm is demonstrated on noisy acoustic data.