Bayesian wavelet de-noising with the caravan prior

According to both domain expert knowledge and empirical evidence, wavelet coefficients of real signals tend to exhibit clustering patterns, in that they contain connected regions of coefficients of similar magnitude (large or small). A wavelet de-noising approach that takes into account such a feature of the signal may in practice outperform other, more vanilla methods, both in terms of the estimation error and visual appearance of the estimates. Motivated by this observation, we present a Bayesian approach to wavelet de-noising, where dependencies between neighbouring wavelet coefficients are a priori modelled via a Markov chain-based prior, that we term the caravan prior. Posterior computations in our method are performed via the Gibbs sampler. Using representative synthetic and real data examples, we conduct a detailed comparison of our approach with a benchmark empirical Bayes de-noising method (due to Johnstone and Silverman). We show that the caravan prior fares well and is therefore a useful addition to the wavelet de-noising toolbox.Comment: 32 pages, 15 figures, 4 table

Spread Divergences

For distributions p and q with different supports, the divergence D(p|q) may not exist. We define a spread divergence on modified p and q and describe sufficient conditions for the existence of such a divergence. We demonstrate how to maximize the discriminatory power of a given divergence by parameterizing and learning the spread. We also give examples of using a spread divergence to train and improve implicit generative models, including linear models (Independent Components Analysis) and non-linear models (Deep Generative Networks)

Approximate Bayesian inference for robust speech processing

Speech processing applications such as speech enhancement and speaker identification rely on the estimation of relevant parameters from the speech signal. Theseparameters must often be estimated from noisy observations since speech signals are rarely obtained in ‘clean’ acoustic environments in the real world. As a result, the parameter estimation algorithms we employ must be robust to environmental factors such as additive noise and reverberation. In this work we derive and evaluate approximate Bayesian algorithms for the following speech processing tasks: 1) speech enhancement 2) speaker identification 3) speaker verification and 4) voice activity detection.Building on previous work in the field of statistical model based speech enhancement, we derive speech enhancement algorithms that rely on speaker dependent priors over linear prediction parameters. These speaker dependent priors allow us to handle speech enhancement and speaker identification in a joint framework. Furthermore, we show how these priors allow voice activity detection to be performed in a robust manner.We also develop algorithms in the log spectral domain with applications in robust speaker verification. The use of speaker dependent priors in the log spectral domain is shown to improve equal error rates in noisy environments and to compensate for mismatch between training and testing conditions.Ph.D., Electrical Engineering -- Drexel University, 201